PHYSICS 9646 - Weeblyscore-in-chemistry.weebly.com/uploads/4/8/7/1/48719755/srjc_2015...PHYSICS 9646 Preliminary ... For each question there are four possible ... = 1.67 x 10 27 kg

SERANGOON JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2

PHYSICS 9646

Preliminary Examination 27 August 2015 Multiple Choice Questions 1 hr 15 mins Additional Materials: OMS.

READ THIS INSTRUCTIONS FIRST

Write your name, civics group and index number in the spaces at the top of this page. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid.

There are forty questions in this section. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the OMS. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

.

This document consists of 18 printed pages and 2 blank pages.

NAME

CG INDEX NO.

2

SRJC 2015 9646/MYE/2015

DATA AND FORMULAE

Data

speed of light in free space, c = 3.00 x 108 m s1

permeability of free space, μ0 = 4π x 10-7 H m-1

permittivity of free space, ε0 = 8.85 x 10-12 F m-1

= (1/(36 π)) x 10-9 F m-1

elementary charge, e = 1.60 x 1019 C

the Planck constant, h = 6.63 x 1034 J s

unified atomic mass constant, u = 1.66 x 1027 kg

rest mass of electron, me = 9.11 x 1031 kg

rest mass of proton, mp = 1.67 x 1027 kg

molar gas constant, R = 8.31 J K1 mol1

the Avogadro constant, NA = 6.02 x 1023 mol1

the Boltzmann constant, k = 1.38 x 10-23J K1

gravitational constant, G = 6.67 x 10-11N m2 Kg2

acceleration of free fall, g = 9.81 m s2

3

SRJC 2015 9646/MYE/2015 [Turn Over

For Examiner’s

Use Formulae

uniformly accelerated motion, s = ut + ½ at2

v2 = u2 + 2as

work done on/by a gas, W = pV

hydrostatic pressure, p = gh

gravitational potential, = GM

-r

displacement of particle in s.h.m., x = x0 sin ωt

velocity of particle in s.h.m., v = v0 cos ωt

= 2 2

0±ω x - x

mean kinetic energy of a molecule E = 3/2 kT

of an ideal gas,

resistors in series, R = R1 + R2 + …

resistors in parallel, 1/R = 1/R1 + 1/R2 + …

electric potential, V = Q/ 4 π ε0r

alternating current/ voltage, x = x0 sin ωt

transmission coefficient, T α exp(-2kd)

where k = 2

2

8 ( - )m U E

h

radioactive decay, x = x0 exp(-λt)

decay constant, λ =

2

1

693.0

t

4

SRJC 2015 9646/PRELIM/2015

Answer all questions

1 Which of the following is a random error?

A Error as a result of using g = 10 m s–2, instead of g = 9.81 m s-2 B Error due to the recording of time using a stopwatch C Error due to a stopwatch running too fast D Zero error of a measuring instrument

2 The relation between the velocity v of waves in the sea with its wavelength , the surface

tension and density of sea water is given by:

kv

where k = constant of proportionality.

If = (4.30 + 0.05) N m-1, = (1450 + 20) kg m-3 and the uncertainty in is 5 %, what is the

percentage uncertainty in the velocity of the waves?

A 2 % B 3 % C 4 % D 8 % 3 A heavy metal ball falls freely under gravity after being released from rest. Which graph best represents the variation of height h of the ball from the ground with time t?

h / m

t / s

A

h / m

t / s

C

h / m

t / s

B

h / m

t / s

D

5


For Examiner’s

Use 4 A ball is fired horizontally from the top of a cliff with a speed of 30 m s-1. Air resistance is

negligible. What will be its speed 3.0 s later?

A 29 m s-1 B 42 m s-1 C 54 m s-1 D 60 m s-1 5 Two blocks with masses 5m and 2m are pushed along a horizontal frictionless surface by a

horizontal applied force F as shown. What is the magnitude of the force exerted by 2m on 5m?

A 2

7F B

2

5F C

5

7F D

5

2F

6 A 1.5 kg clay target is fired at 10 m s-1 into the air at an angle 30° to the horizontal. At its

maximum height, it is hit by a 40 g pellet that was travelling at 50 m s1 vertically upwards. If the pellet was embedded after it hits the clay target, what is the horizontal speed of the combined mass immediately after collision?

A 1.30 m s-1 B 6.17 m s-1 C 8.44 m s-1 D 8.53 m s-1

7 The tension in a spring of natural length lo is first increased from zero to T1, and is then

increased to T2.

Which area of the graph represents the work done by the spring during when the tension increases from T1 to T2? A PQW B PRS C QRSW D SUVW

tension

length

lo P

Q

R S

U

T1 T2 0 V

W

5m 2m F

6

SRJC 2015 9646/PRELIM/2015

8 A uniform beam is hinged at P and is supported by a cable attached to the mid-point of the beam.

What is the direction of the force exerted by the wall on the beam? A PQ B QP C PR D RP

9 Air is enclosed in a cylinder by a gas-tight, frictionless piston of cross-sectional area 25.0 cm2. When a constant external pressure of 3.0 x 104 Pa is exerted on the piston, it settles at a distance from the end of the cylinder.

The gas is then heated and the piston moves 5.0 mm as a result. What is the work done on the gas?

A - 380 J B - 0.38 J C 0.38 J D 380 J

10 A body of mass 5.0 kg is initially travelling at a constant speed of 2.0 m s-1 on a horizontal frictionless surface. A force of 15 N acts on it and accelerates it to a final velocity of 12.0 m s-1. What is the work done by the force?

A 150 J B 180 J C 250 J D 350 J

11 A particle travels in uniform circular motion. Which of the following correctly describes the centripetal force, angular velocity and linear momentum of the particle? centripetal force angular velocity linear momentum A constant constant constant B constant varying constant C varying constant varying D varying varying varying

P

R

Q

cable

beam

wall

gas

3.0 x 104 Pa

piston cylinder

7


For Examiner’s

Use 12 In a frictionless roller coaster ride a car of mass 15 kg, starts from rest at the top of the first

hill at point P of height 20 m. The radius of curvature of the hill at point Q is 9 m.

What will be the magnitude of the force of car on the hill when it reaches the top of the second hill at point Q?

A 32 N B 41 N C 65 N D 82 N

13 A star system consists of 3 stars X, Y and Z, each of mass 4.0 x 1023 kg, positioned at a distance 9.8 x 1013 m about a central star P of mass 7.0 x 1024 kg. Stars X, Y and Z are positioned at a distance 1.7 x 1014 m from each other as shown.

What is the potential at the position that Z is located at?

A − 4.8 J kg−1 B − 5.1 J kg−1 C − 1.9 x 1024 J kg−1 D − 2.0 x 1024 J kg−1

14 A rocket is launched from the surface of a planet with mass M and radius r. What is the

minimum velocity the rocket must be given to completely escape from the planet’s gravitational field?

A GM

r B

2

GM

r C

2GM

r D

2

2GM

r

X

Z Y

P

1.7 x 1014

m

P

Q

20 m

v

18 m

8

SRJC 2015 9646/PRELIM/2015

15 A metal sphere is undergoing a simple harmonic motion. The graph below shows how the acceleration a varies with its displacement x with respect to a fixed point.

Fig. 27 What is the velocity of the metal sphere when the displacement x is 0.25 m?

A 1.0 m s−1 B 1.7 m s−1 C 2.0 m s−1 D 8.0 m s−1

0

a / m s−2

x / m

8.0

0.50

− 8.0

− 0.50

9


For Examiner’s

Use 16 A mass oscillates vertically in water as shown. The support vibrates with a driving frequency which can be varied. Another similar setup is used replacing water with oil.

Which graph best represents the way in which the amplitudes of both cases vary with driving frequency?

17 Ice of mass m at 0 °C is added to water of mass m at 100 °C. Assume that there is no heat

loss to the environment. The specific latent heat of fusion of ice and specific heat capacity of

water are 3.3 105 J kg-1 and 4.2 103 J kg-1 K-1 respectively. What is the final temperature of the mixture? A 11 °C B 21 °C C 79 °C D 89 °C

D C

Driving frequency

Amplitude

Water

Oil

Driving frequency

Amplitude

Oil

Water

Driving frequency

Amplitude

Oil

Water

Driving frequency

Amplitude

Water

Oil

A B

C D

A B

C D

10

SRJC 2015 9646/PRELIM/2015

18 An ideal gas is contained in two spherical containers X and Y of volume 2V and V respectively, connected by a hollow tube of negligible volume. The containers X and Y are maintained at temperatures 2T and T respectively. The setup is shown in the diagram below.

Determine the ratio number of moles of gas in container X

number of moles of gas in container Y.

A 1 : 4 B 1 : 1 C 2 : 1 D 4 : 1

19 A point source of sound emits energy equally in all directions at a constant rate and a person

8 m from the source listens. After a while, the intensity of the source is doubled. If the person wishes the sound to seem as loud as before, how far should he be standing now? A 1.4 m B 4.0 m C 5.7 m D 11.3 m

20 A sound wave travelling towards the right through air causes the air molecules to be

displaced from their original positions. The graph below shows the variation with distance of the displacement of air molecules at a particular instant of time.

Taking the displacement towards the right as positive, at which point is the pressure maximum?

X

Y

2V

2T

V T

distance

displacement

A

B

C

D

11


For Examiner’s

Use 21 A signal from source S is emitted through two separate speakers as shown below. The sound

waves from the speakers reach a point P by two paths which differ in length by 1.4 m. When the frequency of the sound is gradually increased, the resultant intensity at P goes through a series of maxima and minima. A maximum occurs when the frequency is 1000 Hz and the next maximum occurs at 1200 Hz.

What is the speed of the sound waves?

A 200 m s-1

B 240 m s-1

C 280 m s-1

D 330 m s-1

22 Interference maxima produced by a double source are observed at a distance of 1.0 m

from the sources. In which one of the following cases are the maxima closest together?

A sound waves of wavelength 20 mm from sources 50 mm apart

B surface water waves of wavelength 10 mm from sources 200 mm apart

C blue light from sources 2.0 mm apart

D red light from sources 4.0 mm apart

23 Two horizontal metal plates, each of length 100 mm, are separated by a distance D. The

potential difference between the two plates is 2.0 V, as shown below.

If an electron situated between the two plates experiences an electric force of 6.4 1016 N upwards, what are the direction of the electric field and the distance between the two plates, D? A Upwards, 0.25 mm B Upwards, 0.50 mm C Downwards, 0.25 mm D Downwards, 0.50 mm

100 mm

2.0 V electron

S

P

12

SRJC 2015 9646/PRELIM/2015

24 The diagram below is a scaled drawing showing the equipotential lines in the region of an electric field.

Which point has an electric field strength of the greatest magnitude?

A N B R C T D U

25 The figure below shows the top view of a metal strip of uniform thickness. The width of the narrow section is half the width of the wider section.

Which of the following statements is correct? A The potential difference per unit length of the narrower section is the same as the

potential difference per unit length of the wider section. B The potential difference per unit length of the narrower section is smaller than the

potential difference per unit length of the wider section. C The resistance of the narrower section will be smaller and hence more current will flow

through as compared to the wider section. D The resistance per unit length of the narrow section is twice that of the wide section.

current

13


For Examiner’s

Use 26 A battery of e.m.f E with internal resistance r, supplies a current of 0.025 A for 80 s.

During this time, it produces 18 J of electrical energy while the resistor P receives 11 J and resistor Q receives 4 J.

What are the values for r and E ? r E A 60 Ω 360 V B 60 Ω 9.0 V C 300 Ω 9.0 V D 300 Ω 360 V 27 An e.m.f source of 6.0 V, with internal resistance 1.0 Ω is connected across a load which

consists of two resistors in parallel. The resistance of the variable resistor R may be varied from 1.0 Ω to 6.0 Ω.

What is the resistance of R for maximum power to be delivered to the load?

A 1 Ω B 2 Ω C 3 Ω D 6 Ω

6.0 V 1.0

R

2.0

E r

P

Q

14

SRJC 2015 9646/PRELIM/2015

28 The circuit below shows a potentiometer circuit with the jockey adjusted to position J, where balance point is achieved.

Which one of the following statements is correct?

A The balance length will be longer than WJ if switch B is opened. B The balance length will be longer than WJ if wire WX is replaced with another wire of

the same length but higher resistivity C The balance length will be shorter than WJ if switch A is closed. D The balance length will be shorter than WJ if E decreased.

29 Two wires carry the same amount of current flowing into the page. Which of the following

diagrams shows the resultant magnetic field pattern in the region?

D C

A B

E

1

W

E2

X J

r1

switch A r2

R

Y Z

switch B

15


For Examiner’s

Use 30 A beam of electrons travelling at 5.0 106 m s1 enter a magnetic field of magnetic flux

density 6.0 mT at right angles to it. What is the radius of the path of the electrons within the magnetic field?

A 4.74 ×10-6 m B 4.74 ×10-3 m C 8.70 ×10-3 m D 8.70 m

31 A 15 MW nuclear power station produces electrical power at 500 V. It uses a step-up ideal

transformer with a turns ratio of 1 : 100 to increase the voltage before transmitting it over long-distance cables of total resistance 20 Ω. What is the power lost as heat in the cables?

A 1.25 W B 1.80 ×106 W C 1.25 ×108 W D 1.80 x 1014 W

32 The figure below shows a copper disc rotating at a constant frequency about its centre O in

a uniform magnetic field between two bar magnets. The magnetic field is acting perpendicularly to the disc.

Which of the following graphs correctly shows the variation of the induced e.m.f. E between the centre O and a point R on the rim of the disc with time t?

33 The average power dissipated in a resistor of resistance R supplied with alternating current

of peak value Io is P. What is the r.m.s value of the alternating current supplied for a resistor 4R to dissipate an average power of 8P ?

A Io B 2 Io C 2Io D 4Io

South pole O

R

North pole

E

t

E

t

E

t

E

t

A B

C D

16

SRJC 2015 9646/PRELIM/2015

34 The circuit shows a sinusoidal a.c. generator connected to five ideal diodes and a resistor R. P and Q are connected to the y-plates of a cathode ray oscilloscope.

Which of the following traces would be seen? A B

C D

35 In a photoelectric experiment, the following graph of stopping potential, VS, against the

frequency of the electromagnetic radiation, f, is initially obtained, as denoted by the solid line.

The photoemissive material is then changed to one with a lower work function.

Which of the following graphs represents the new relationship between VS and f?

stopping potential, VS

frequency of EM radiation, f 0

A D B C

P

Q

R

17


For Examiner’s

Use 36 An electron is incident on a potential barrier as shown below.

The probability that a particle of mass m and energy E will tunnel through a barrier of height 10 eV and thickness L is given by the transmission coefficient T.

Which of the following set of values below will give the highest probability of the electron being transmitted?

E/ eV L/ nm A 4 0.2 B 4 0.4 C 8 0.4

D 8 0.2 37 Which of the following statements about electron transitions between energy levels is true?

A Spontaneous emission occurs more rapidly when the lifetime of the excited state is long.

B Stimulated emission occurs more rapidly when the stimulating photon beam is of high intensity.

C Stimulated emission describes a scenario when an atom get ‘excited’ from a lower energy state E1 to a higher energy state E2 when one of its electron absorbs a photon of energy E2 – E1.

D Stimulated emission is always preferred over stimulated absorption in a 2-level laser system.

38 Which of the following statements is/are correct? I. The charge carriers in an n-type semiconductor are electrons. II. The charge carriers in an n-type semiconductor are holes. III. An n-type semiconductor is negatively-charged. A I only B I & III only C I & II only D All

Energy

Electron

U

nE

n

L

n

x

18

SRJC 2015 9646/PRELIM/2015

39 The equation

235 1 121 113 1

92 0 45 47 0U + n Rh + Ag + 2 n

shows the fission of a Uranium−235 nuclide by a slow-moving neutron into a Rhodium-121 nuclide, a Silver-113 nuclide and two neutrons.

binding energy per nucleon of 235

92U = 7.59 MeV


45Rh = 8.26 MeV


47 Ag = 8.52 MeV

What is the energy released during this fission process?

A 9.19 MeV

B 24.4 MeV

C 73.9 MeV

D 179 MeV

40 A high energy -particle collides with a N147 nucleus to produce a O17

8 nucleus.

What could be the other products of this collision? A a -photon alone

B a -photon and a -particle

C a -photon and a neutron

D a -photon and a proton

End of Paper

19


For Examiner’s

Use

BLANK PAGE

20

SRJC 2015 9646/PRELIM/2015

BLANK PAGE


PHYSICS 9646

Preliminary Examination 27 August 2015 Multiple Choice Questions 1 hr 15 mins Additional Materials: OMS.


Write your name, civics group and index number in the spaces at the top of this page. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid.

There are forty questions in this section. Answer all questions. For each question there are four possible answers A, B, C and D. Choose the one you consider correct and record your choice in soft pencil on the OMS. Each correct answer will score one mark. A mark will not be deducted for a wrong answer. Any rough working should be done in this booklet.

.

This document consist of 20 printed pages and 0 blank page.

NAME

CG INDEX NO.

2

SRJC 2015 9646/MYE/2015

DATA AND FORMULAE

Data




= (1/(36 π)) x 10-9 F m-1











3


For Examiner’s

Use Formulae


v2 = u2 + 2as




-r



= 2 2

0±ω x - x


of an ideal gas,






where k = 2

2

8 ( - )m U E

h



2

1

693.0

t

4

SRJC 2015 9646/PRELIM/2015

Answer all questions

1 Which of the following is a random error?

A Error as a result of using g = 10 m s–2, instead of g = 9.81 m s-2 B Error due to the recording of time using a stopwatch C Error due to a stopwatch running too fast D Zero error of a measuring instrument

2 The relation between the velocity v of waves in the sea with its wavelength , the surface

tension and density of sea water is given by :

kv

where k = constant of proportionality.

If = (4.30 + 0.05) N m-1, = (1450 + 20) kg m-3 and the uncertainty in is 5 %, what is

the percentage uncertainty in the velocity of the waves?

A 2 % B 3 % C 4 % D 8 %

3 A heavy metal ball falls freely under gravity after being released from rest. Which graph best represents the variation of height h of the ball from the ground with time t?

h / m

t / s

A

h / m

t / s

C

h / m

t / s

B

h / m

t / s

D

Ans: C

Percentage uncertainty in v = %41001450

20100

3.4

05.05

2

1

Ans: B A, C and D are systematic errors.

5


For Examiner’s

Use 4 A ball is fired horizontally from the top of a cliff with a speed of 30 m s-1. Air resistance is

negligible. What will be its speed 3.0 s later?

A 29 m s-1 B 42 m s-1 C 54 m s-1 D 60 m s-1

5 Two blocks with masses 5m and 2m are pushed along a horizontal frictionless surface by a

horizontal applied force F as shown. What is the magnitude of the force exerted by 2m on 5m?

A 2

7F B

2

5F C

5

7F D

5

2F

6 A 1.5 kg clay target is fired at 10 m s-1 into the air at an angle 30° to the horizontal. At its

maximum height, it is hit by a 40 g pellet that was travelling at 50 m s1 vertically upwards. If

the pellet was embedded after it hits the clay target, what is the horizontal speed of the

combined mass immediately after collision?

A 1.30 m s-1 B 6.17 m s-1 C 8.44 m s-1 D 8.53 m s-1

Ans: A F = 5ma + 2ma = 7ma Let force acted on 5m by 2m be FX. Considering 5m block, F - FX = 5ma 7ma - FX = 5ma FX = 2ma

Ans: B 1

2 2 2 2 1

0 (9.81)(3) 29.4 m s

30 29.4 42 m s

y y

x y

v u at

v v v

Ans: D Let ho be the initial height of the ball above the ground.

2 2

2

1 1

2 2

1

2

o

o

h h ut gt gt

h h gt

5m 2m F

6

SRJC 2015 9646/PRELIM/2015

7 The tension in a spring of natural length lo is first increased from zero to T1, and is then

increased to T2.

Which area of the graph represents the work done by the spring during when the tension

increases from T1 to T2?

A PQW

B PRS

C QRSW

D SUVW

Ans: D By conservation of momentum, Horizontal direction M ux1 + m ux2 = (M + m)vx

1.5 (10 cos 30°) + 0 = (1.5 + 0.040) vx

vx = 8.435 m s 1

Ans: C Work done by spring = Elastic potential energy stored in spring =Area under force-extension graph

tension

length

lo P

Q

R S

U

T1 T2 0 V

W

7


For Examiner’s

Use

8 A uniform beam is hinged at P and is supported by a cable attached to the mid-point of the beam.

What is the direction of the force exerted by the wall on the beam? A PQ B QP C PR D RP

9 Air is enclosed in a cylinder by a gas-tight, frictionless piston of cross-sectional area

25.0 cm2. When a constant external pressure of 3.0 x 104 Pa is exerted on the piston, it

settles at a distance from the end of the cylinder.

The gas is then heated and the piston moves 5.0 mm as a result. The work done on the gas is

A - 380 J B - 0.38 J C 0.38 J D 380 J

P

R

Q

cable

beam

wall

Ans: A All 3 forces (tension, weight and force by wall on beam) should pass through a common point of intersection, which is at the midpoint of the beam.

weight tension

force by wall on beam weight

tension

force by wall on beam

gas

3.0 x 104 Pa

piston cylinder

Ans: B

Gas is expanding, hence work is done by the gas.

Work done by gas = p ΔV = 3.0 x 104 x 25 x 10-4 x 5 x 10-3 = 0.38 J

Work done on gas = - Work done by gas = - 0.38 J

8

SRJC 2015 9646/PRELIM/2015

10 A body of mass 5.0 kg is initially travelling at a constant speed of 2.0 m s-1 on a horizontal

frictionless surface. A force of 15 N acts on it and accelerates it to a final velocity of 12.0 m s-1.

What is the work done by the force?

A 150 J B 180 J C 250 J D 350 J 11 A particle travels in uniform circular motion. Which of the following correctly describes the centripetal force, angular velocity and linear momentum of the particle? Centripetal force angular velocity linear momentum A constant constant constant B constant varying constant C varying constant varying D varying varying varying

12 In a frictionless roller coaster ride a car of mass 15 kg, starts from rest at the top of the first hill at point P of height 20 m. The radius of curvature of the hill at point Q is 9 m.

What will be the magnitude of the force of car on the hill when it reaches the top of the second hill at point Q?

A 32 N B 41 N C 65 N D 82 N

Ans: C For uniform circular motion, angular velocity is constant. Centripetal force and linear

velocity/momentum are constant in magnitude but varying direction

Ans : D

By COE from point A to B, Ep = Ek mg(20 – 18) = ½ m v2 ; v = 6.26 ms-1

F => W – R = m v2 / r R = W - m v2 / r = mg - m v2 / r =82 N

P

Q

20 m

v

18 m

Ans: D WD by force = gain in KE = ½ mv2 - ½ mu2 = ½ (5)(12)2 - ½ (5)(2)2 = 350 J

9


For Examiner’s

Use 13 A star system consists of 3 stars X, Y and Z, each of mass 4.0 x 1023 kg, positioned at a

distance 9.8 x 1013 m about a central star P of mass 7.0 x 1024 kg. Stars X, Y and Z are positioned at a distance 1.7 x 1014 m from each other as shown.

What is the potential at the position that Z is located at?

A − 4.8 J kg−1

B − 5.1 J kg−1

C − 1.9 x 1024 J kg−1

D − 2.0 x 1024 J kg−1

14 A rocket is launched from the surface of a planet with mass M and radius r. What is the minimum velocity the rocket must be given to completely escape from the planet’s gravitational field?

A GM

r B

2

GM

r C

2GM

r D

2

2GM

r

X

Z Y

P

1.7 x 1014

m

Ans: B

. .

. .

.

11 23 11 24

14 13

1

2

2 6 67 10 4 10 6 67 10 7 10

1 7 10 9 8 10

5 1

Z X Y P

X Y P

xz yz pz

X P

xz pz

GM GM GM

r r r

GM GM

r r

Jkg

Ans: C Loss in KE = Gain in GPE

21 mv - 0 0

2

2 v

GMm

r

GM

r

10

SRJC 2015 9646/PRELIM/2015

15 A metal sphere is undergoing a simple harmonic motion. The graph below shows how the

acceleration a varies with its displacement x with respect to a fixed point.

Fig. 27

What is the velocity of the metal sphere when the displacement x is 0.25 m?

A 1.0 m s−1 B 1.7 m s−1 C 2.0 m s−1 D 8.0 m s−1

Ans: B amax = 8.0 m s−2

As particle is undergoing simple harmonic motion,

8 = - (-0.5)ω2

ω = 4 rad s-1

v =22

xxo

v = 22 25.05.04

Speed v = 1.7 m s−1

0

a / m s−2

x / m

8.0

0.50

− 8.0

− 0.50

11


For Examiner’s

Use 16 A mass oscillates vertically in water as shown. The support vibrates with a driving frequency

which can be varied. Another similar setup is used replacing water with oil.

Which graph best represents the way in which the amplitudes of both cases vary with driving frequency?

D C

Driving frequency

Amplitude

Water

Oil

Driving frequency

Amplitude

Oil

Water

Driving frequency

Amplitude

Oil

Water

Driving frequency

Amplitude

Water

Oil

A B

C D

A B

C D

Ans: A Increased damping when water replaced by oil. Hence lower amplitude and lower

frequency for setup with oil

12

SRJC 2015 9646/PRELIM/2015

17 Ice of mass m at 0 °C is added to water of mass m at 100 °C. Assume that there is no heat loss to the environment. The specific latent heat of fusion of ice and specific heat capacity of

water are 3.3 105 J kg-1 and 4.2 103 J kg-1 K-1 respectively. What is the final temperature of the mixture? A 11 °C B 21 °C C 79 °C D 89 °C

18 An ideal gas is contained in two spherical containers X and Y of volume 2V and V

respectively, connected by a hollow tube of negligible volume. The containers X and Y are maintained at temperatures 2T and T respectively. The setup is shown in the diagram below.

Determine the ratio number of moles of gas in container X

number of moles of gas in container Y.

A 1 : 4 B 1 : 1 C 2 : 1 D 4 : 1

X

Y

2V

2T

V T

Ans: A

Let the final temperature be . Heat gained by ice = heat lost by water

ml + mc = mc(100-)

(3.3 105) + (4.2 103) = (4.2 103)(100-)

= 11 °C

Ans: B

Container X: 2

2

X X X XX Y X X X

X

n RT n R T n RTp V n RT p

V V V

Container Y: Y Y YY Y Y Y Y

Y

n RT n RTp V n RT p

V V

Since X Yp p ,

X Yn n , 1X

Y

n

n .

13


For Examiner’s

Use 19 A point source of sound emits energy equally in all directions at a constant rate and a person

8 m from the source listens. After a while, the intensity of the source is doubled. If the person wishes the sound to seem as loud as before, how far should he be standing now? A 1.4 m B 4.0 m C 5.7 m D 11.3 m

20 A sound wave travelling towards the right through air causes the air molecules to be displaced from their original positions. The graph below shows the variation with distance of the displacement of air molecules at a particular instant of time.

Taking the displacement towards the right as positive, at which point is the pressure

maximum?

Ans: D Initially, I = 2

2

akr

When intensity is doubled at the same distance, I1 = 2

2

(a 2 )kr

For intensity to be same at distance r1 from source; 2

2

1

(a 2 )kr

= 2

2

akr

r1 = 8 2 = 11.3 m

distance

displacement

A

B

C

D

Ans: A

Since displacement towards the right is taken as positive, we can label the directions of displacement of air molecules as follows:

It can be seen from the figure that at point A, it is a region of compression as air molecules on the left side of A is displaced to the right and on the right side of A, they are displaced to the

left. Hence A has the maximum pressure.

Distance

Displacement

A

B

C

D

14

SRJC 2015 9646/PRELIM/2015

21 A signal from source S is emitted through two separate speakers as shown below. The sound waves from the speakers reach a point P by two paths which differ in length by 1.4 m. When the frequency of the sound is gradually increased, the resultant intensity at P goes through a series of maxima and minima. A maximum occurs when the frequency is 1000 Hz and the next maximum occurs at 1200 Hz.

What is the speed of the sound waves?

A 200 m s-1

B 240 m s-1

C 280 m s-1

D 330 m s-1

22 Interference maxima produced by a double source are observed at a distance of 1.0 m

from the sources. In which one of the following cases are the maxima closest together?

A sound waves of wavelength 20 mm from sources 50 mm apart

B surface water waves of wavelength 10 mm from sources 200 mm apart

C blue light from sources 2.0 mm apart

D red light from sources 4.0 mm apart

S

P

𝑛 = 1.4

𝑛 (𝑣

𝑓1) = 1.4 𝑛 (

𝑣

1000) = 1.4 𝑛 =

1400

𝑣 − −(1)

(𝑛 + 1) (𝑣

𝑓2) = 1.4 (𝑛 + 1) (

𝑣

1200) = 1.4 − −(2)

Ans: C

For constructive interference,

Solving (1) and (2), v = 280 m s-1

Ans: D Maxima closest = Fringe separation, x, is the smallest

Using 𝑥 = 𝜆𝐷

𝑎

For same D, x ∝ 𝜆

𝑎

Smallest 𝜆

𝑎 ratio is option D

15


For Examiner’s

Use 23 Two horizontal metal plates, each of length 100 mm, are separated by a distance D. The

potential difference between the two plates is 2.0 V, as shown below.

If an electron situated between the two plates experiences an electric force of 6.4 1016 N upwards, what are the direction of the electric field and the distance between the two plates, D?

A Upwards, 0.25 mm

B Upwards, 0.50 mm

C Downwards, 0.25 mm

D Downwards, 0.50 mm

24 The diagram below is a scaled drawing showing the equipotential lines in the region of an

electric field.

Which point has an electric field strength of the greatest magnitude?

A N B R C T D U

100 mm

2.0 V electron

Ans: D

mmmF

Vqdq

d

VEqF 5.00005.0

104.6

106.12)(

16

19

Ans: C The electric field strength is greatest when the potential gradient is largest, ie. when the equipotential lines are closest together.

16

SRJC 2015 9646/PRELIM/2015

25 The figure below shows the top view of a metal strip of uniform thickness. The width of the narrow section is half the width of the wider section.

Which of the following statements is correct?

A The potential difference per unit length of the narrower section is the same as the

potential difference per unit length of the wider section.

B The potential difference per unit length of the narrower section is smaller than the

potential difference per unit length of the wider section.

C The resistance of the narrower section will be smaller and hence more current will flow

through as compared to the wider section.

D The resistance per unit length of the narrow section is twice that of the wide section.

current

Ans: D

Since l

l l

R RR

A A A

1

(ρ is constant for same material), resistance

per unit length of the narrow section is twice that of wide section since the constant

current flows through the narrower section.

Since V R for constant I, the resistor with the larger resistance has a larger p.d.

across it. Hence, the narrower section (with larger resistance per unit length), has larger

p.d. per unit length across it. Hence option A and B are wrong

Same current flows through the strip by Kirchoff’s 1st Law, hence D is incorrect.

17


For Examiner’s

Use 26 A battery of e.m.f E with internal resistance r, supplies a current of 0.025 A for 80 s. During

this time, it produces 18 J of electrical energy while the resistor P receives 11 J and resistor Q receives 4 J.

What are the values for r and E ?

r E A 60 Ω 360 V B 60 Ω 9.0 V C 300 Ω 9.0 V D 300 Ω 360 V

E r

P

Q

Ans: B

. ( )

.

( . )

2

2

18 0 025 80

9 0

Energy dissipated by r = 18-11-4=3J

3

30 025 60

80

W IEt

E

E V

I rt

r r

18

SRJC 2015 9646/PRELIM/2015

27 An e.m.f source of 6.0 V, with internal resistance 1.0 Ω is connected across a load which consists of two resistors in parallel. The resistance of the variable resistor R may be varied from 1.0 Ω to 6.0 Ω.

What is the resistance of R for maximum power to be delivered to the load?

A 1 Ω B 2 Ω C 3 Ω D 6 Ω

28 The circuit below shows a potentiometer circuit with the jockey adjusted to position J, where

balance point is achieved.

Which one of the following statements is correct?

A The balance length will be longer than WJ if switch B is opened.

B The balance length will be longer than WJ if wire WX is replaced with another wire of

the same length but higher resistivity

C The balance length will be shorter than WJ if switch A is closed.

D The balance length will be shorter than WJ if E decreased.

6.0 V 1.0

R

2.0

Ans: B

For maximum power to be delivered to the load, the effective resistance is 1 and

hence R = 2 .

E

1

W

E2

X J

r1

switch A r2

R

Y Z

switch B

19


For Examiner’s

Use

29 Two wires carry the same amount of current flowing into the page. Which of the following

diagrams shows the resultant magnetic field pattern in the region?

D C

A B

Ans: D Using Right Hand Grip, the magnetic field around each wire is in clockwise direction. There is a neutral point between the wire.

Ans: A Statement A is correct as with switch B opened, the balanced length attained will have the p.d. equal to emf E2. Hence, balanced length will be longer.

Statement B is incorrect as Rwx increases, Vwx increases. Hence shorter balance length

Statement C is incorrect as with switch A closed, the p.d. across the wire is lower and hence, a longer balanced length is required.

Statement D is incorrect as with E decreased, Vwx decreases and hence, a longer balanced length is required.

20

SRJC 2015 9646/PRELIM/2015

30 A beam of electrons travelling at 5.0 106 m s1 enter a magnetic field of magnetic flux density 6.0 mT at right angles to it. What is the radius of the path of the electrons within the magnetic field?

A 4.74 ×10-6 m B 4.74 ×10-3 m C 8.70 ×10-3 m D 8.70 m

31 A 15 MW nuclear power station produces electrical power at 500 V. It uses a step-up ideal

transformer with a turns ratio of 1: 100 to increase the voltage before transmitting it over

long-distance cables of total resistance 20 Ω. What is the power lost as heat in the cables?

A 1.25 W B 1.80 ×106 W C 1.25 ×108 W D 1.80 ×1014 W

Ans: B Electromagnetic force provides centripetal force 2

31 63

3 19

(9.11 10 )(5.0 10 )4.74 10 m

(6 10 )(1.6 10 )

mvBqv

r

mvr

Bq

Ans: B

100500

50000 V

S S

P P

S

S

V N

V N

V

V

Since the transformer is ideal,

6

6

2 2 6

15 10

15 10300 A

50000

P 300 (20) 1.80 10 W

S S

S

loss S cable

V I

I

I R

21


For Examiner’s

Use 32 The figure below shows a copper disc rotating at a constant frequency about its centre O in

a uniform magnetic field between two bar magnets. The magnetic field is acting perpendicularly to the disc.

Which of the following graphs correctly shows the variation of the induced e.m.f. E between the centre O and a point R on the rim of the disc with time t?

South pole O

R

North pole

E

t

E

t

E

t

E

t

A B

C D

Ans: A

π

2

2

since 1, and is already

since constant

dE

dt

dE BA N B A

dt

dAB B

dt

rB

T

E B r f

The induced e.m.f. is constant across OR.

22

SRJC 2015 9646/PRELIM/2015

33 The average power dissipated in a resistor of resistance R supplied with alternating current

of peak value Io is P.

What is the r.m.s value of the alternating current supplied for a resistor 4R to dissipate an average power of 8P ?

A Io B 2 Io C 2Io D 4Io

34 The circuit shows a sinusoidal a.c. generator connected to five ideal diodes and a resistor R.

P and Q are connected to the y-plates of a cathode ray oscilloscope.

Which of the following trace would be seen? A B

C D

Ans: A 2 2

2 o orms

I I RP I R R

22

implies 2P / R = Io

2

R'IP'2

rms

'

' 2

rms8P I 4R

' 2 2

rms o

8P 2I I

4R

P

R

o

'

rms II

P

Q

R

Ans: C

23


For Examiner’s

Use 35 In a photoelectric experiment, the following graph of stopping potential, VS, against the

frequency of the electromagnetic radiation, f, is initially obtained, as denoted by the solid line.

The photoemissive material is then changed to one with a lower work function.

Which of the following graphs represents the new relationship between VS and f?

stopping potential, VS

frequency of EM radiation, f 0

A D B C

Ans : A By linearising Einstein’s photoelectric equation:

where grad = h/e, y-int = hfo/e and x-int = fo

Hence, gradient remains constant while the x-int decreases.

oS

hfhfV

e e

24

SRJC 2015 9646/PRELIM/2015

36 An electron is incident on a potential barrier as shown below.

The probability that a particle of mass m and energy E will tunnel through a barrier of height

10 eV and thickness L is given by the transmission coefficient T.

Which of the following set of values below will give the highest probability of the electron

being transmitted?

E/ eV L/ nm

A 4 0.2

B 4 0.4

C 8 0.4

D 8 0.2 37 Which of the following statements about electron transitions between energy levels is true?

A Spontaneous emission occurs more rapidly when the lifetime of the excited state is long.

B Stimulated emission occurs more rapidly when the stimulating photon beam is of high intensity.

C Stimulated emission describes a scenario when an atom get ‘excited’ from a lower energy state E1 to a higher energy state E2 when one of its electron absorbs a photon of energy E2 – E1.

D Stimulated emission is always preferred over stimulated absorption in a 2-level laser system.

Ans : B A should be when the lifetime is short. C should be stimulated absorption. D is only true provided that there is population inversion.

Energy

Electron

U

nE

n

L

n

x

Ans : D The higher the electron energy and the smaller the barrier width, the higher the probability of transmission.

25


For Examiner’s

Use 38 Which of the following statements is/are correct? I. The charge carriers in an n-type semiconductor are electrons. II. The charge carriers in an n-type semiconductor are holes. III. An n-type semiconductor is negatively-charged. A I only B I & III only C I & II only D All 39 The equation

235 1 121 113 1

92 0 45 47 0U + n Rh + Ag + 2 n

shows the fission of a Uranium−235 nuclide by a slow-moving neutron into a Rhodium-121 nuclide, a Silver-113 nuclide and two neutrons.


92U = 7.59 MeV


45Rh = 8.26 MeV


47 Ag = 8.52 MeV

What is the energy released during this fission process?

A 9.19 MeV

B 24.4 MeV

C 73.9 MeV

D 179 MeV

40 A high energy -particle collides with a N147 nucleus to produce a O17

8 nucleus.

What could be the other products of this collision? A a -photon alone

B a -photon and a -particle

C a -photon and a neutron

D a -photon and a proton

Ans: D Energy released = BEproduct - BEreactant

= [8.26(121) + 8.52(113)] – 7.59(235) = 179 MeV

Ans: D By conservation of charge and mass numbers,

HOHeN 11

178

42

147

Therefore, one of the products must be a proton.

Ans : C III is not correct as an n-type semiconductor is electrically neutral.

26

SRJC 2015 9646/PRELIM/2015

End of Paper


PHYSICS 9646

Preliminary Examination 21 August 2015 Paper 2 Structured Questions 1 hour 45 min Candidates answer on the Question Paper. Additional material – Answer Booklet for Question 7.


Write your name, civics group and index number in the spaces at the top of this page. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid.

Answer all questions. At the end of the examination, fasten all your work securely together. The number of marks is given in bracket [ ] at the end of each question or part question. .

This document consists of 19 printed pages and 1 blank page

For Examiners’ Use

Q1 / 10

Q2 / 8

Q3 / 9

Q4 / 9

Q5 / 9

Q6 / 15

Q7 / 12

Total marks

/ 72

NAME

CG INDEX NO.

2

SRJC 2015 9646/PRELIM/2015

DATA AND FORMULAE

Data




= (1/(36 π)) x 10-9 F m-1











3

SRJC 2015 9646/PRELIM/2015 [Turn Over

For Examiner’s

Use Formulae


v2 = u2 + 2as




-r



= 2 2

0±ω x - x


of an ideal gas,






where k = 2

2

8 ( - )m U E

h



2

1

693.0

t

4

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

1 (a) A boy of height 1.6 m throws a stone from a height of 0.2 m above his head to hit a

coconut from a tree that is 7.0 m away from him as shown in Fig 1.1. At the instant

the coconut drops vertically downwards from the tree, he throws the stone at a

speed of 15 m s-1 at an angle of 10° to the horizontal. Air resistance is negligible.

Fig 1.1

(i) Show that the time taken for the stone to hit the coconut is 0.474 s. [1]

(ii) Calculate the initial vertical distance of the coconut on the tree from the

ground, x.

x = ……..…………. m [3]

7.0 m

1.6 m

0.2 m

15 m s-1

10°

x

5


For Examiner’s

Use (iii) In practice, there is air resistance. Explain how the time taken for the stone

to reach the maximum height changes as compared to when there is no air

resistance.

………………………………………………………………………………………

………………………………………………………………………………………

………………………………………………………………………………………

…..………………………………………..……………………………………… [2]

(b) The boy now throws a stone of mass 0.5 kg vertically downwards at a speed of

6.0 m s-1 from a very tall building. The air resistance acting on the stone is given by

R = kv2 where v is the speed of the stone.

(i) State Newton’s Second Law.

………………………………………………………………………………………

………………………………………………………………………………………

………………………………………………………………………………………

…..………………………………………..……………………………………… [2]

(ii) The initial deceleration is 15 m s-2. Show that the value of k is 0.345. [1]

(i) Show that the terminal velocity of the stone is 3.77 m s-1. [1]

6

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

2 (a) Two balls of masses 1 kg and 3 kg respectively, are suspended from two light

inextensible strings.

The balls are connected by a light spring of spring constant 15 N m-1 and rest in

equilibrium as shown in Fig. 2.1.

Two forces, X and Y are then simultaneously applied to the 1 kg and 3 kg balls

respectively as shown in Fig. 2.2. The 1 kg ball is displaced from its equilibrium

position to the left by 0.2 m, while the 3 kg ball is displaced from its equilibrium

position to the right by 0.3 m.

(i) Calculate the force in the spring.

force = ……..…………. N [2]

(ii) Calculate the magnitude of the force Y.

Y = ……..…………. N [3]

1 kg 3 kg

Fig. 2.1

Y

1 kg 3 kg

Fig. 2.2

X

25°

0.2 m 0.3 m

7


For Examiner’s

Use

(b) A 20 kg narrow column AB is hinged at point A and is held stationary in position as

shown in Fig. 2.3. The 5.0 m long column has its centre of gravity X at a distance of

3.0 m from point A. The column makes an angle of 40° to the horizontal and is

connected to a rope which makes an angle of 25° to the column.

(i) Calculate the tension T in the rope.

T = ……..…………. N [2]

(ii) A golden eagle lands on point X of the column AB. Suggest one change to

be made to the set-up in order for the tension, as well as the angle between

the rope and the column to remain the same.

………………………………………………………………………………………

…..………………………………………..……………………………………… [1]

Fig. 2.3

rope X

A

3.0 m

5.0 m

40°

25°

B

8

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

3 A battery of e.m.f. 4.50 V and negligible internal resistance is connected with a uniform

resistance wire PQ of length 1.00 m and 2 fixed resistors of resistance 1200 Ω and 1800 Ω

respectively as shown in Fig. 3.1. A sensitive voltmeter is connected between point B and a

moveable contact M on the wire.

Fig. 3.1

(a) By reference to energy transfer, distinguish between electromotive force (e.m.f.) and

potential difference (p.d.).

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……..………………………..……………………..………………………………………… [2]

(b) Show that, for constant current in the wire, the potential difference V between any two

points on the wire is proportional to the distance between the points. [2]

1800 Ω

4.50 V

9


For Examiner’s

Use

(c) The contact M is moved along PQ until the voltmeter shows zero reading.

(i) Calculate the potential difference between the contact at M and the point Q.

potential difference = …………………………. V [2]

(ii) Calculate the length of wire between M and Q.

length = ………………………….. m [2]

(iii) The battery was replaced by an alternating source of peak value of 4.50 V. State the change (if any) to the mean power delivered to the circuit.

...................................................................................................................................

....................................................................................................................................

..................................................................................................................................[1]

10

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

4 A rectangular metal loop PQRS of dimensions 14.0 cm x 10.0 cm and resistance 12 Ω

moves at constant speed of 2.0 cm s-1 through a region of uniform magnetic field WXYZ with

magnetic field strength B of 1.5 T as shown in the top view in Fig. 4.1.

(a) (i) State the direction of induced current in the loop PQRS.

……………………..……………………..………………………………………………… [1]

(ii) Calculate the maximum induced e.m.f. in the loop PQRS.

maximum induced e.m.f. = ……..…………. V [2]

(iii) A force is applied to the side QR to move the loop PQRS into the uniform magnetic

field. Explain why the loop does not accelerate but moves with constant velocity

once it is in the magnetic field.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

……..………………………..……………………..……………………………………… [2]

R

Q

2.0 cm s-1

P

S

14.0 cm

10.0 cm

Fig. 4.1

W

X

Y Z

B

11


For Examiner’s

Use (iv) Calculate the force applied to the side QR for it to move with the constant velocity in

(a)(iii).

force = ……..…………. N [2]

(b) The metal loop is now tilted at an angle of 25° to the horizontal as shown in the side

view in Fig. 4.2.

Fig. 4.2

State and explain how the magnitude of the force applied to the side QR will

change, if so, for it to still move with constant velocity.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

……..………………………..……………………..……………………………………… [2]

25°

B

S

R

2 cm s-1

12

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

5(a)(i) State 2 features of the electron energy levels in an isolated atom that lead to distinct

lines in a line spectrum.

……………………………………………………………………………………………………

……………………………………………………………………………………………..………

……………………………………………………………………………………………….… [2]

(ii) Describe how the appearance of an absorption line spectrum is different from an

emission line spectrum.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………….………………… [2]

(b) Although protons and electrons are usually treated as particles, they also possess

“wave” characteristics, which can be exploited by transmission microscopes to obtain

high-resolution images of extremely small objects. For instance, electrons with a de

Broglie wavelength of 4.5 nm can be used by such microscopes to image the structure

of viruses.

(i) Show that the de Broglie wavelength of a particle, in terms of its mass, m and

its kinetic energy, E, is

2

h

mE

[1]

(ii) Hence, determine the kinetic energy of an electron which has a de Broglie

wavelength of 4.5 nm.

energy = ……………………….. J [2]

13


For Examiner’s

Use (iii) The resolution of an image can be improved by using particles with shorter de

Broglie wavelengths.

Suggest and explain one way to decrease the de Broglie wavelength.

………………………………………………………………………………………………

………………………………………………………………………………………………

…..……………………………………………………………..……………………………

………………………………………………………………………………………………

……………………………………………………………………………...………..… [2]

14

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

6 An air-track is a scientific device used to study motion. Air is pumped through a hollow track

with fine holes along the track to allow specifically fitted air-track cars to glide relatively

friction-free.

(a) A force F is applied to car A, which is initially stationary, as shown in Fig. 6.1. Car A attains

a speed of v1 at the instant when the force is removed from car A.

Fig. 6.1

The variation of the force F with time t is shown in Fig. 6.2. The maximum magnitude of the

force during the time period is Fmax. Three trials are conducted with varying Fmax.

Fig. 6.2

(i) Express v1 in terms of Fmax and m1, the mass of car A. [2]

(ii) The mass of car A, m1, is 0.5 kg. Complete the table in Fig. 6.3. [2]

Trial Fmax / N Change in momentum / kg m s-1 v1 / m s-1

1 10.0

2 20.0

3 50.0

Fig. 6.3

car A

force F

air-track

v1

0 0.10 0.20 0.30 t / s

F / N

10.0

20.0

30.0

40.0

50.0

60.0

Trial 1

Trial 2

Trial 3

15


For Examiner’s

Use (b) Car A then glides along the air-track and moves towards car B, which has a light sticky tape.

Car B has a mass of m2 and is initially stationary, as shown in Fig. 6.4.

Fig. 6.4

Both cars coalesce after collision and the combined body glides along the air-track with

speed v2 as shown in Fig. 6.5.

Fig. 6.5

(i) Express v1 in terms of m1, m2, and v2. [2]

car A

air-track

v1

car B

initially stationary

sticky tape

car A

air-track

v2 car B

16

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

(ii) When Fmax in part (a) is 10.0 N, the variation of momentum of car A and car B with

time respectively is shown in Fig. 6.6.

Fig. 6.6

The mass of car A, m1, is 0.5 kg. Show that m2 is 0.6 kg. [2]

0 0.500 1.000 1.500 2.500 t / s

p / kg m s-1

0.400

0.200

0.600

1.000

0.800

1.200

car A

2.000 3.000

car B

17


For Examiner’s

Use (c) A student conducts an experiment to investigate the relationship between Fmax in part (a)

with the speed of the combined body, v2, in part (b). He conducts three sets of experiments

when the mass of Car B, m2, is varied. His experimental results are shown in Fig. 6.7.

Fig. 6.7

(i) With the aid of answers from parts (a)(i) and (b)(i), show that the gradient of the

graph is 10(m1 + m2). [1]

(ii) State which graph (X or Y) represents m2 that is greater than 0.6 kg.

………………………………………………………………………………………………[1]

(iii) The mass of car A, m1, is 0.5 kg. Calculate m2 for graph X.

m2 = ……………………….. kg [2]

0 2.00 4.00 6.00 8.00 10.00

v2 / m s-1

Fmax / N

40

80

120

m2 = 0.6 kg

Graph X

Graph Y

18

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

(iv) With reference to Fig. 6.7, suggest one source of error in this experiment.

………………………………………………………………………………………

………………………………………………………………………………………………[1]

(v) The experimental error in part (c)(iv) is removed. Sketch on Fig. 6.7, the variation of

Fmax with v2, when the mass of Car B is 0.4 kg. Label this graph Z. [2]

19


For Examiner’s

Use 7 Write your answer on the Answer Booklet provided.

A hot wire in air loses energy. This energy lost depends on the number of particles hitting the

wire per second, and hence on the air pressure.

If the temperature of the wire is constant, then the total energy lost per second is equal to the

electrical energy supplied per second.

Design a laboratory experiment to investigate how the total energy lost per second from a wire

depends on the air pressure.

You may assume that the following apparatus is available, together with any other standard

equipment which may be found in a school or college science laboratory.

Mercury thermometer

Thermocouple

Bell jar (Fig. 7.1)

Gas pump

Vacuum pump

Pressure gauge

Flow meter

Direct current power source

Variable power supply

Voltmeter

Ammeter

Rheostat

Signal Generator

Cathode-ray Oscilloscope

Fig. 7.1

You should draw a detailed labelled diagram showing the arrangement of your equipment. In

your account you should pay particular attention to:

(a) the procedure to be followed,

(b) how the electrical energy supplied to the wire per second would be measured,

(c) the type of thermometer used to check that the temperature of the wire remains

constant during the experiment,

(d) how the pressure would be changed and measured,

(e) any safety precautions that you would take.

[12]

20

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

BLANK PAGE


PHYSICS 9646

Preliminary Examination 21 August 2015 Paper 2 Structured Questions 1 hour 45 min Candidates answer on the Question Paper. No Additional Materials are required.



Answer all questions. At the end of the examination, fasten all your work securely together. The number of marks is given in bracket [ ] at the end of each question or part question. .

This document consist of 20 printed pages and 0 blank page


Q1 / 10

Q2 / 8

Q3 / 9

Q4 / 9

Q5 / 9

Q6 / 15

Q7 / 12

Total marks

/ 72

NAME

CG INDEX NO.

2

SRJC 2015 9646/PRELIM/2015

DATA AND FORMULAE

Data




= (1/(36 π)) x 10-9 F m-1











3


For Examiner’s

Use Formulae


v2 = u2 + 2as




-r



= 2 2

0±ω x - x


of an ideal gas,






where k = 2

2

8 ( - )m U E

h



2

1

693.0

t

4

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

Section A

Answer all the questions in this section.

1 (a) A boy of height 1.6 m throws a stone from a height of 0.2 m above his head to hit a

coconut from a tree that is 7.0 m away from him as shown in Fig 1.1. At the instant

the coconut drops vertically downwards from the tree, he throws the stone at a

speed of 15 m s-1 at an angle of 10° to the horizontal. Air resistance is negligible.

Fig 1.1

(i) Show that the time taken for the stone to hit the coconut is 0.474 s. [1]

(ii) Calculate the initial vertical distance of the coconut on the tree from the

ground, x.

x = ……..…………. m [3]

sx = (u cos θ) t 7.0 = 15 cos 10° t [B1] t = 0.474 s

x = distance of coconut above boy’s hand + distance of coconut from its initial position at the instant it is hit + 1.6 + 0.2

2 21 1[(15sin10 ) ] 1.8

2 2

[B1] [B1] [B1]

3.03 m

t gt gt

7.0 m

1.6 m

0.2 m

15 m s-1

10°

x

5


For Examiner’s

Use (iii) In practice, there is air resistance. Explain how the time taken for the stone

to reach the maximum height changes as compared to when there is no air

resistance.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

……..………………………..……………………..……………………………………… [2]

(b) The boy now throws a stone of mass 0.5 kg vertically downwards at a speed of

6.0 m s-1 from a very tall building. The air resistance acting on the stone is given by

R = kv2 where v is the speed of the stone.

(i) State Newton’s Second Law.

………………………………………………………………………………………

………………………………………………………………………………………

………………………………………………………………………………………

…..………………………………………..……………………………………… [2]

(ii) The initial deceleration is 15 m s-2. Show that the value of k is 0.345. [1]

(i) Show that the terminal velocity of the stone is 3.77 m s-1. [1]

The net force acting and hence the downward acceleration on the stone when there is air resistance as compared to no air resistance is larger. [M1 - accept either net force or acceleration] OR The stone does work against air resistance, causing less of the kinetic energy to become gravitational potential energy and stone to reach a lower maximum height. [M1] Hence, time taken for vertical velocity to become zero is less than when there is no air resistance. [A1]

Using Newton’s 2nd Law Fnet = R – mg = ma [must be stated] kv2 – mg = ma k = [m(a+g)] / v2 = [0.5(15+9.81)]/62 [B1] =0.345

Terminal velocity occurs when Fnet =0 Fnet = R – mg = 0 kvT

2 – mg = 0

1

0.5(9.81) [M1]

0.345

=3.77 m s

T

mgv

k

Newton’s Second Law states that the rate of change of momentum of a body is directly proportional to the magnitude of the resultant force acting on it [B1], and the change of momentum takes place in the direction of the resultant force.[B1]

6

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

2 (a) Two balls of masses 1 kg and 3 kg respectively, are suspended from two light

inextensible

strings. The balls are connected by a light spring of spring constant 15 N m-1 and

rest in equilibrium as shown in Fig. 2.1.

Two forces, X and Y are then simultaneously applied to the 1 kg and 3 kg balls

respectively as shown in Fig. 2.2. The 1 kg ball is displaced from its equilibrium

position to the left by 0.2 m, while the 3 kg ball is displaced from its equilibrium

position to the right by 0.3 m.

(i) Calculate the force in the spring.

force = ……..…………. N [2]

(ii) Calculate the magnitude of the force Y.

1 kg 3 kg

Fig. 2.1

Y

1 kg 3 kg

Fig. 2.2

X

25°

0.2 m 0.3 m

Taking upwards as positive Sum of forces in vertical direction = 0

cos25 0 [M1]

3(9.81)32.5 N

cos25

T W

T

Taking rightwards as positive Sum of forces in horizontal direction = 0

sin25 0 [M1]

32.5sin25 7.5 0

Y=21.2 N [A1]

SY T F

Y

Y

T

Fs

W

Fs = kx = 15 (0.2+0.3) [M1] = 7.5 N [A1]

7


For Examiner’s

Use Y = ……..…………. N [3]

(b) A 20 kg narrow column AB is hinged at point A and is held stationary in position as

shown in Fig. 2.3. The 5.0 m long column has its centre of gravity X at a distance of

3.0 m from point A. The column makes an angle of 40° to the horizontal and is

connected to a rope which makes an angle of 25° to the column.

(i) Calculate the tension T in the rope.

T = ……..…………. N [2]

(ii) A golden eagle lands on point X of the column AB. Suggest one change to

be made to the set-up in order for the tension, as well as the angle between

the rope and the column to remain the same.

………………………………………………………………………………………

…..………………………………………..……………………………………… [1]

Principle of Moments Taking moments about the base Sum of clockwise moments = Sum of anti-clockwise moments mg (3.0 cos 40°) = T (5.0 sin 25°) [M1] T = 213 N [A1]

Increase the angle between the column and the horizontal. [B1] The anti-clockwise moment about point A due to tension remains the same. When the eagle lands on the column, its weight would contribute to the clockwise moment about point A. (mcolumn + meagle) g (3.0 cos θ) = T (5.0 sin 25°) cos θ must be reduced, and hence θ increases.

Fig. 2.3

rope X

A

3.0 m

5.0 m

40°

25°

B

8

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

3 A battery of e.m.f. 4.50 V and negligible internal resistance is connected with a uniform resistance wire PQ of length 1.00 m and 2 fixed resistors of resistance 1200 Ω and 1800 Ω respectively as shown in Fig. 3.1. A sensitive voltmeter is connected between point B and a moveable contact M on the wire.

Fig. 3.1

(a) By reference to energy transfer, distinguish between electromotive force (e.m.f.) and

potential difference (p.d.).

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

……..………………………..……………………..……………………………………… [2]

(b) Show that, for constant current in the wire, the potential difference V between any two

points on the wire is proportional to the distance between the points. [2]

For a uniform wire, resistance R = ρL/A where ρ= resistivity of the wire, A=cross-sectional area of wire V = I x (ρL/A) [M1] I, ρ and A are constant [A1]

hence V ∝ L [minus 1 mark if did not define symbols that are not stated in question]

1800 Ω

The electromotive force (e.m.f.) of a source is defined using the energy converted from non-electrical to electrical [B1] per unit charge delivered round a complete circuit while potential difference between two points is defined using energy converted

from electrical to non- electrical per unit charge passing from one point to the

other.

. [B1]

9


For Examiner’s

Use

(c) The contact M is moved along PQ until the voltmeter shows zero reading.

(i) Calculate the potential difference between the contact at M and the point Q.

potential difference = …………………………. V [2]

(ii) Calculate the length of wire between M and Q.

length = ………………………….. m [2]

(iii) The battery was replaced by an alternating source of peak value of 4.50 V. State the change (if any) to the mean power delivered to the circuit.

……...................................................................................................................................

..........................................................................................................................................

....................................................................................................................................... [1]

p.d across M and Q = p.d across thermistor

=

18004.50

1800 1200 [M1]

= 2.70 V [A1]

since V ∝ L

2.70 [M1]

4.5 1.00

0.60 [A1]

QM QM

PQ PQ

QM

QM

V L

V L

L

L m

Mean power decreases. [B1]

10

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

4 A rectangular metal loop PQRS of dimensions 14.0 cm x 10.0 cm and resistance 12 Ω

moves at constant speed of 2.0 cm s-1 through a region of uniform magnetic field WXYZ with

magnetic field strength B of 1.5 T as shown in the top view in Fig. 4.1.

(a) (i) State the direction of induced current in the loop PQRS.

……………………..……………………..………………………………………………… [1]

(ii) Calculate the maximum induced e.m.f. in the loop PQRS.

maximum induced e.m.f. = ……..…………. V [2]

(iii) A force is applied to the side QR to move the loop PQRS into the uniform magnetic

field. Explain why the loop does not accelerate but moves with constant velocity

once it is in the magnetic field.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

……..………………………..……………………..……………………………………… [2]

(iv) Calculate the force applied to the side QR for it to move with the constant velocity in

(iii).

force = ……..…………. N [2]

R

Q

2.0 cm s-1

P

S

14.0 cm

10.0 cm

Fig. 4.1

When the rod QR cuts the magnetic field, an induced current flows in it, a magnetic force is produced on QR [B1], The magnetic force on QR is in opposite direction and equal in magnitude to the applied force, resulting in no net force and hence acceleration. [B1] OR No change in flux linkage to the loop [B1], hence there is no induced e.m.f. and induced current though the loop. No net force and hence acceleration. [B1]

Fext = FB = BIl = B(E/R) l = 1.5 (3×10-3 /12)(0.10) [M1]

= 3.75 ×10-5 N [A1]

Emax = Blv = 1.5 (0.10)(0.02) [M1] = 3×10-3 V [A1]

W

X

Y Z

B

Anti-clockwise. [A1]

11


For Examiner’s

Use

(b) The metal loop is now tilted at an angle of 25° to the horizontal as shown in the side

view in Fig. 4.2.

Fig. 4.2

State and explain how the magnitude of the force applied to the side QR will

change, if so, for it to still move with constant velocity.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………………………………………………

……..………………………..……………………..……………………………………… [2]

25°

B

S

R

2 cm s-1

There is a decrease in - the magnetic flux density perpendicular to the area OR - the magnetic flux density perpendicular to the velocity OR - the rate of cutting of flux

[M1] Hence, the force is smaller [A1]

12

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

5(a)(i) State 2 features of the electron energy levels in an isolated atom that lead to distinct lines in a line spectrum.

……………………………………………………………………………………………………

……………………………………………………………………………………………..………

……………………………………………………………………………………………….… [2]

(ii) Describe how the appearance of an absorption line spectrum is different from an

emission line spectrum.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………….………………… [2]

(b) Although protons and electrons are usually treated as particles, they also possess

“wave” characteristics, which can be exploited by transmission microscopes to obtain

high-resolution images of extremely small objects. For instance, electrons with a de

Broglie wavelength of 4.5 nm can be used by such microscopes to image the structure

of viruses.

(i) Show that the de Broglie wavelength of a particle, in terms of its mass, m and its kinetic energy, E, is

= ℎ

√2𝑚𝐸

[1]

(i) Hence, determine the kinetic energy of an electron which has a de Broglie

wavelength of 4.5 nm.

energy = ……………………….. J [2]

An absorption spectrum has separate dark lines superimposed on a

continuous colored background [B1], whereas an emission spectrum

has separate differently coloured lines against a black background

[B1].

Electron energy levels are fixed [B1] and discrete [B1].

= h/p but E = p2/2m [B1 for first two lines]

Hence, p = (2mE)

Therefore = h/(2mE)

Using = h/(2mE)

4.5 x 10-9 = 6.63 x 10-34 / (2 x 9.11 x 10-31 x E) [M1] E = 1.19 x 10-20 J [A1]

13


For Examiner’s

Use (ii) The resolution of an image can be improved by using particles with shorter de

Broglie wavelengths. Suggest and explain one way to decrease the de Broglie wavelength.

……………………………………………………………………………………………

……………………………………………………………………………………………

………..……………………………………………………………..……………………

……………………………………………………………………………………………

…………………………………………………………………………...………..… [2]

Since = h/2mE,

If the kinetic energy E of the particle is increased [B1], will be reduced. This can be done by accelerating the electrons through a larger potential difference [B1]. Or

If we use a particle with a larger mass [B1], would also be reduced. Hence, use protons instead. [B1]

14

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

6 An air-track is a scientific device used to study motion. Air is pumped through a hollow track

with fine holes along the track to allow specifically fitted air-track cars to glide relatively

friction-free.

(a) A force F is applied to car A, which is initially stationary, as shown in Fig. 6.1. Car A attains

a speed of v1 at the instant when the force is removed from car A.

Fig. 6.1

The variation of the force F with time t is shown in Fig. 6.2. The maximum magnitude of the

force during the time period is Fmax. Three trials are conducted with varying Fmax.

Fig. 6.2

(i) Express v1 in terms of Fmax and m1, the mass of car A.

[2]

max 1 1

max1

1

Area under F-t graph = Impulse = Change in momentum

1(0.2) 0 [M1]

2

[A1]10

F m v

Fv

m

car A

force F

air-track

v1

0 0.10 0.20 0.30 t / s

F / N

10.0

20.0

30.0

40.0

50.0

60.0

Trial 1

Trial 2

Trial 3

15


For Examiner’s

Use

(ii) The mass of car A, m1, is 0.5 kg. Complete the table in Fig. 6.3. [2]

Trial Fmax / N Change in momentum / kg m s-1 v1 / m s-1

1 10.0

2 20.0

3 50.0

Fig. 6.3

(b) Car A then glides along the air-track and moves towards car B, which has a light sticky tape.

Car B has a mass of m2 and is initially stationary, as shown in Fig. 6.4.

Fig. 6.4

Both cars coalesce after collision and the combined body glides along the air-track with

speed v2 as shown in Fig. 6.5.

Fig. 6.5

(i) Express v1 in terms of m1, m2, and v2. [2]

1 2 2 4 5 10

car A

air-track

v1

car B

initially stationary

sticky tape

car A

air-track

v2 car B

1 1 1 2 2

1 21 2

1

Principle of conservation of linear momentum

Taking rightwards as positive

v +0 ( ) [M1]

( ) [A1]

m m m v

m mv v

m

Deduct 0.5 mark for each mistake. Deduct 2 marks max

16

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

(ii) When Fmax in part (a) is 10.0 N, the variation of momentum of car A and car B with

time respectively is shown in Fig. 6.6.

Fig. 6.6

The mass of car A, m1, is 0.5 kg. Show that m2 is 0.6 kg. [2]

0.455

0.4550.910 [M1]

0.5

0.545 (0.910) [M1]

0.6 kg

A

A B

B B B B

B

p

v v

p m v m

m

0 0.500 1.000 1.500 2.500 t / s

p / kg m s-1

0.400

0.200

0.600

1.000

0.800

1.200

car A

2.000 3.000

car B

17


For Examiner’s

Use (c) A student conducts an experiment to investigate the relationship between Fmax in part (a)

with the speed of the combined body, v2, in part (b). He conducts three sets of experiments

when the mass of Car B, m2, is varied. His experimental results are shown in Fig. 6.7.

Fig. 6.7

(i) With the aid of answers from parts (a)(i) and (b)(i), show that the gradient of the

graph is 10(m1 + m2). [1]

(ii) State which graph (X or Y) represents m2 that is greater than 0.6 kg.

………………………………………………………………………………………………[1]

From (a)(i)

max1

1

(equation 1) 10

Fv

m

From b(i)

1 21 2

1

( ) (equation 2)

m mv v

m

Equation 1 = Equation 2

max 1 22

1 1

max 1 2 2

( )

10

10( )

F m mv

m m

F m m v

[M1]

The gradient is 10(m1 + m2).

0 2.00 4.00 6.00 8.00 10.00

v2 / m s-1

Fmax / N

40

80

120

m2 = 0.6 kg

Graph X

Graph Y

Graph Y [B1]

Z

18

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

(iii) The mass of car A, m1, is 0.5 kg. Calculate m2 for graph X. [2]

(iv) With reference to Fig. 6.7, suggest one source of error in this experiment.

………………………………………………………………………………………

………………………………………………………………………………………………[1]

(v) The experimental error in part (c)(iv) is removed. Sketch on Fig. 6.7, the variation of

Fmax with v2, when the mass of Car B is 0.4 kg. Label this graph Z. [2]

90 108.0

10.00 0

ygradient

x

[M1]

gradient = 10(m1 + m2) 8.0 = 10 (0.5 + m2) m2 = 0.3 kg [A1]

The equipment measuring Fmax has a systematic error – consistent zero error. [B1] OR There is a constant friction on the air track. [B1]

Graph passes through the origin [B1] with gradient = 9 [B1]

19


For Examiner’s

Use 7 A hot wire in air loses energy. This energy lost depends on the number of particles hitting the

wire per second, and hence on the air pressure.

If the temperature of the wire is constant, then the total energy lost per second is equal to the

electrical energy supplied per second.

Design a laboratory experiment to investigate how the total energy lost per second from a wire

depends on the air pressure.

You may assume that the following apparatus is available, together with any other standard

equipment which may be found in a school or college science laboratory.

Mercury thermometer

Thermocouple

Bell jar (Fig. 7.1)

Gas pump

Vacuum pump

Pressure gauge

Flow meter

Direct current power source

Variable power supply

Voltmeter

Ammeter

Rheostat

Signal Generator

Cathode-ray Oscilloscope

Fig. 7.1

You should draw a detailed labelled diagram showing the arrangement of your equipment. In

your account you should pay particular attention to:

(a) the procedure to be followed,

(b) how the electrical energy supplied to the wire per second would be measured,

(c) the type of thermometer used to check that the temperature of the wire remains

constant during the experiment,

(d) how the pressure would be changed and measured,

(e) any safety precautions that you would take.

[12]

20

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

Suggested Write-up Diagram

Procedure

(1) Set up apparatus as shown above.

(2) Measure the pressure (p) within the bell jar using a pressure gauge.

(3) Close the switch.

(4) Measure the voltmeter reading (V) and the ammeter reading (I).

(5) Measure the temperature (T) of the wire within the bell jar, after it has stabilized,

using a thermocouple.

(6) Open the switch and allow the wire in the jar to cool down.

(7) Repeat steps (3) to (6) for further readings using different values of pressure within

the bell jar (Use the vacuum pump and valve to vary and fix the pressure within the

bell jar). The rheostat should be adjusted to change the power supplied to wire such

that the same temperature T is obtained.

(8) Calculate the energy supplied per second using Power P = IV

(9) Assume that the power supplied P and gas pressure p are related by the equation

P = k pn , ln P = ln k + n ln p. Hence, plot a graph of ln P against ln p. If a straight

line graph is obtained, then the relationship is valid, with gradient = n and y-intercept

= ln k.

In this experiment, the air pressure surrounding the wire is varied, while the temperature of the wire is kept constant. Additional precautions to improve quality of results:

Leave the circuit to cool before starting again.

Repeat readings to obtain an average

V

A

Pressure

gauge

To vacuum pump

Needle valve Heated

wire

Thermocouple

Bell Jar

ice

21


For Examiner’s

Use Safety precautions

Wear gloves to prevent getting burnt when handling the hot wire

Increase the pressure slowly and do not set too high a pressure in case the bell jar shatter under high pressure

Suggested Mark Scheme

Procedure [max 4]

Electrical arrangement: Correct circuit using ammeter and voltmeter.

Mechanical arrangement: The wire must be shown inside a closed container

Mechanical arrangement: Means of changing the pressure (e.g. air pump, vacuum pump)

Measure pressure and electrical power; change pressure and measure new power and repeat

Measurement [max 3]

Measurement of pressure (e.g. pressure gauge)

Power supplied to wire = V x I

Use of thermocouple to monitor temperature whilst pressure is changed

Control of variables [max 1]

Change setting on the power supply to keep the wire at the same temperature when the pressure

is changed.

Keep external temperature constant to ensure power loss to environment is the same

Data Analysis [max 1]

Plot a graph of ln P against ln p.

If a straight line graph is obtained, then the relationship P = k pn is valid, with gradient = n and y-

intercept = ln k.

Safety Considerations [max 1]

e.g. safety screens/goggles/wire mesh surrounding vacuum chamber

Pressure must not be too high or too low

Additional Detail for Improved Accuracy/Precision [max 2]

Multimeter or voltmeter connected to thermocouple, or mention of calibration

Use of valve to control pressure.

Allow time between readings for experiment to stabilise.

Do not allow the wire to become too hot or the thermocouple may melt.

Means of controlling power supplied.

End of Paper

22

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

BLANK PAGE

23


For Examiner’s

Use END OF PAPER


PHYSICS 9646

Preliminary Examination 24 Aug 2015 Paper 3 Longer Structured Questions 2 hours Candidates answer on the Question Paper. No Additional Materials are required.



Section A Answer all questions. Section B Answer any two questions. You are advised to spend about an hour on each section. At the end of the examination, fasten all your work securely together. The number of marks is given in bracket [ ] at the end of each question or part question. .

This document consist of 26 printed pages and 2 blank pages.


Q1 / 8

Q2 / 9

Q3 / 7

Q4 / 8

Q5 / 8

Q6 / 20

Q7 / 20

Q8 / 20

Total marks

/ 80

NAME

CG INDEX NO.

2

SRJC 2015 9646/MYE/2015

DATA AND FORMULAE

Data




= (1/(36 π)) x 10-9 F m-1











3


For Examiner’s

Use Formulae


v2 = u2 + 2as




-r



= 2 2

0±ω x - x


of an ideal gas,






where k = 2

2

8 ( - )m U E

h



2

1

693.0

t

4

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

Section A


1 (a) State the First Law of Thermodynamics.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [1]

(b) An ideal gas is placed in an insulated cylinder as shown in Fig. 1.1.

Fig 1.1

Initially, its pressure is 1.04 x 105 Pa and its temperature is 314 K. 28.6 J of heat is then

applied to the gas, causing its volume to increase from 2.9 x 10-4 m3 to 4.0 x 10-4 m3

while keeping its pressure constant.

(i) Calculate the work done on the gas.

work done on gas = ……………………….. J [2]

(ii) Show that the change in internal energy of the gas is 17.2 J.

change in internal energy = ……………………….. J [1]

piston

gas

5


For Examiner’s

Use (iii) Calculate the new temperature of the gas given that it has 6.96 × 1021

molecules.

new temperature = ……………………….. K [2]

(iv) Calculate the ratio of the final r.m.s. speed to the original r.m.s. speed of the

molecules.

ratio = ……………………….. [2]

6

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

r /106 m

0 5.0 10.0 15.0 20.0 25.0

10.0

8.0

6.0

4.0

2.0

0

g /N kg−1

2 (a) Fig. 2.1 shows a graph of the variation of the gravitational field strength g of the Earth

with distance r from its centre.

Fig. 2.1

(i) State the relationship between gravitational field strength g and gravitational potential Φ.

……………..………………..…………………………………………………….……...…… [1]

(ii) Define gravitational potential energy.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [1]

(iii) Hence, estimate the work done in bringing a mass of 5.0 kg from r = 25 x 106 m

to r = 10 x 106 m.

work done = ………………………….. J [3]

7


For Examiner’s

Use (b) A star system consists of 3 stars X, Y and Z, each of mass 4.0 x 1022 kg, moving with

the same speed and in the same direction in a circular orbit of radius 9.8 x 1013 m about a central star P of mass 7.0 x 1024 kg. Stars X, Y and Z are always positioned at a distance 1.7 x 1014 m from each other as shown in Fig. 2.2.

Fig. 2.2

(i) By considering all the forces acting on X, show that the acceleration of X is

4.9 x 10−14 m s−2. [3]

(ii) Comment on the work done in bringing a unit mass from X to Y.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [1]

X

Z Y

P

1.7 x 1014

m

8

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

3 A block of wood of mass 1.2 kg and cross sectional area of 80 cm2 floats in still water of density 1000 kg m−3 as shown in Fig. 3.1. The height of the portion of the block submerged in water is 15.0 cm.

Fig. 3.1

The block is then pushed down into the water through a depth of 7.0 cm. When the block is released, the block bobs up and down in water. The acceleration of the block a is given by the expression

a = − 65.4x

where x is the vertical displacement from its floating position. (a) Show that the frequency of oscillation of the block is 1.29 Hz. [1]

(b) Calculate the additional upthrust when the block was pushed down from its floating position.

additional upthrust = ………………………….. N [2]

Water trough

Block of wood

9


For Examiner’s

Use (c) On Fig. 3.2, sketch a labelled graph of additional upthrust against the vertical

displacement from the block’s floating position x. [1]

Fig. 3.2

(d) Hence, calculate the total energy of the oscillation.

total energy = ………………………….. J [2]

(e) Surface water waves of speed 0.90 m s−1 are then incident on the block. These cause resonance in the up-and-down motion of the block.

Calculate the wavelength of the water waves.

wavelength = ………………………….. m [1]

Additional upthrust / N

x / m 0 0.07

10

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

4 The Principle of Conservation of Energy can be used to calculate the stopping and

accelerating potentials in the Photoelectric Experiment and generation of X-rays respectively.

(a) (i) Using the Principle of Conservation of Energy, explain Einstein’s Photoelectric

equation: hf = + ½mvmax2

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

(ii) In a photoelectric experiment, the work function of a photoemissive material is

1.3 eV and the wavelength of the light is 550 nm.

Calculate the value of the stopping potential.

stopping potential = ……………………….. V [2]

(b) (i) Using the Principle of Conservation of Energy, derive the expression for the

minimum wavelength of the continuous X-ray spectrum in terms of the

accelerating potential between the anode and the cathode, V. [2]

11


For Examiner’s

Use (ii) Fig. 4.1 shows the X-ray spectrums of an X-ray tube with tungsten and barium as

the anodes respectively.

Fig 4.1

1. State whether the accelerating potentials to produce the X-ray spectra for both tungsten and barium are the same or different.

…….………………………………………..…………………………………………... [1]

2. Calculate the accelerating potential for the tungsten spectrum.

accelerating potential = ………………………. V [1]

12

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

5 Fig. 5.1 shows the I-V characteristic of a semiconductor diode.

Fig. 5.1

(a) State how the resistance of the diode changes when the potential difference applied

across it:

(i) decreases from 0 V (i.e. becomes more negative)

……………………………………………………………………………………………………

…………………………………………………………………………………………………[1]

(ii) increases from Vo

……………………………………………………………………………………………………

…………………………………………………………………………………………………[1]

Vo

V 0

I

13


For Examiner’s

Use (b) The semiconductor diode is made up of a p-n junction.

(i) Describe qualitatively the origin of the depletion region at a p-n junction when a

p-type semiconductor and an n-type semiconductor are brought together.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [4]

(ii) With reference to the depletion region, explain why the resistance of the diode is

as stated in (a)(ii) when a potential difference of greater than Vo is applied across

it.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

14

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

Section B

Answer two questions from this section.

6 (a) Describe, with a labelled diagram, an experiment to determine the speed of sound

using stationary waves.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [5]

15


For Examiner’s

Use (b) In Fig. 6.1 below, a string which is connected to an oscillator at one end, is held down

by a weight at the other end.

(i) The frequency of the oscillator is adjusted such that a stationary wave with its

second lowest resonant frequency is formed. On Fig. 6.2 below, draw a diagram

to represent this mode of vibration. [1]

(ii) The weight is then adjusted such that the speed of the wave along the string is

doubled from (b)(i), while the settings of the oscillator remain unchanged.

On Fig. 6.3 below, draw a diagram to represent this mode of vibration. [1]

(iii) If the speed of the wave along the string in (b)(ii) is 3.5 m s-1, and the distance between the oscillator and the pulley is 3.0 m, determine the fundamental frequency.

fundamental frequency = .................................. Hz [2]

oscillator weight

pulley

direction of oscillation

Fig. 6.1

oscillator weight

pulley


Fig. 6.2

oscillator weight

pulley


Fig. 6.3

16

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

(c) During a fireworks display, a firework explodes high in the air as shown in Fig. 6.4. Two

detectors X and Y are 450 m and 150 m respectively away from the source of the

fireworks. Assume that the sound wave spreads out uniformly in all directions and

reflections from the ground and energy losses in the air can be ignored.

The sound that reaches detector X has an intensity of 0.20 W m-2 and amplitude of A.

(i) Determine, for detector Y,

1. the intensity of the sound detected.

intensity = .......................... W m-2 [2]

2. the amplitude of the sound detected in terms of A.

amplitude = ......................... A [2]

(ii) Determine the ratio surface area of detector X

surface area of detector Y such that both detectors receive

the same amount of power.

ratio = ……………… [2]

X Y

450 m 150 m

fireworks

Fig. 6.4

17


For Examiner’s

Use

(d) In a simple experiment to find out the wavelength of monochromatic red light emitted

by a laser, a fine beam of red laser light is shone through a diffraction grating as shown

below in Fig 6.5.

The diffraction grating has 300 000 lines per metre and is set so that its plane is normal

to the incident light. Bright spots of first and second orders are observed at 0.46 m and

1.00 m respectively, from the central spot on a screen which is 2.00 m from the grating.

(i) From the first-order diffracted light, estimate the wavelength of the laser light.

wavelength = ……………………….. m [3]

(ii) State and explain an advantage of obtaining the wavelength of the laser light by

using the second-order diffracted light rather than the first-order diffracted light.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

Fig 6.5

laser

grating

2.00 m

0.46 m

1.00 m

18

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

7 (a) (i) Define electric field strength.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [1]

(ii) Define electric potential.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [1]

19


For Examiner’s

Use (b) Two charged solid metal spheres A and B are situated in a vacuum. Their centres are

separated by a distance of 12.0 cm, as illustrated in Fig. 7.1. The diagram is not to

scale.

Point P is a point on the line joining the centres of the two spheres. Point P is a

distance x from the centre of sphere A.

The variation with distance x of the electric field strength E at point P is shown in

Fig. 7.2. A positive value of E on the graph at a point corresponds to an electric field

vector pointing horizontally to the right.

Fig. 7.2

Fig. 7.1

20

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

(i) State and explain:

1. the signs of charges of A and B.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

2. the ratio of the radius of sphere A to that of sphere B.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

3. how the electric potential varies inside spheres A and B.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

(ii) A student is interested to find out how the electric potential changes for different

locations of point P.

1. It is given that the ratio of the charges of spheres A and B respectively is

numerically 4:1.

If the electric field strength when x = 4.0 cm is 1.25 × 107 N C-1, calculate

the numerical values of the charges of spheres A and B respectively.

charge of sphere A = ………………………. C

charge of sphere B = ………………………. C [3]

21


For Examiner’s

Use

2. Hence, show that the electric potential at the point P when x = 8.0 cm is

4.0 x 105 V. [1]

3. Using (i) 2, (i) 3 and (ii) 2, sketch on Fig. 7.3 the graph of electric potential

energy of an electron against x, labelling the electric potential energy at

point P where x = 8.0 cm.

The numerical values of electric potential energy of the electron when it is

at the surfaces of both spheres are not required. [3]

Fig. 7.3

EPE / J

x / cm

22

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

(iii) The student places an electron at x = 10.0 cm and releases it.

1. State and explain which sphere the electron will move towards.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [1]

2. Describe and explain the respective changes to the electron’s kinetic

energy and electric potential energy.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

3. Hence or otherwise, calculate the final speed of the electron just before it

hits the sphere as stated in (b)(iii)1. The electric potential at x = 10.0 cm is

4.8 x 1019 V, while the electric potentials at the surfaces of spheres A and B

are 1.6 x 1020 V and 1.1 x 1020 V respectively.

speed = ………………………. m s-1 [2]

23


For Examiner’s

Use 8 (a) The binding energy per nucleon of a cobalt-60 ( Co27

60 ) nuclide is 8.74 MeV. Some rest

mass information is also shown below.

Rest mass of a neutron = 1.008665 u

Rest mass of a proton = 1.007825 u

Rest mass of an electron = 0.000549 u

(i) Calculate, to 5 decimal places, the rest mass of cobalt-60 in terms of u.

rest mass = …………………… u [3]

(ii) Fig. 8.1 shows the process of decay where Cobalt-60 undergoes nuclear decay

to form the stable isotope nickel-60. In the process of decay, Cobalt-60 emits one

beta particle with an energy of 310 keV and then two gamma rays with energies

of 1.17 MeV and 1.33 MeV respectively.

1. Write down the number of protons and neutrons in the nickel nuclide

produced when the cobalt-60 nuclide decays.

number of protons = ……………………

number of neutrons = ……………………. [1]

Fig. 8.1

60

27Co

310 keV ()

1.17 MeV ()

1.33 MeV ()

60Ni

24

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

2. By considering the rest mass of the energy components (beta particle and

gamma rays), calculate, to 5 decimal places, the rest mass of the stable

nickel nuclide in terms of u.

rest mass = …………………… u [3]

3. In practice, the above radioactive decay of cobalt-60 could be used for the

treatment of cancer.

Suggest and explain which type of radiation of the decay is used for the

purpose of tumour treatment.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

4. A. On Fig. 8.2, sketch a graph to show the variation of binding energy

per nucleon with nucleon number, and mark the binding energy per

nucleon of a cobalt-60 nuclide on the graph. [2]

Fig. 8.2

nucleon number

binding energy per nucleon / MeV

25


For Examiner’s

Use

B. Hence, state and explain the nuclear process a nuclide of nucleon

number 120 will most likely undergo.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

(b) A carbon-14 14

6C nuclide undergoes spontaneous and random beta decay to

transform into a stable nitrogen-14 14

7N nuclide.

14 14 0

6 7 -1C N+ β

(i) Explain the terms spontaneous and random.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

(ii) The nuclide of carbon-14 has a half-life of 5730 years. If a carbon-14 source

emits n β-particles in one second today, calculate the time taken for the source to

emit the same number of beta particles 10,000 years later.

time taken = ………………. s [2]

26

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

(iii) Show that the number of undecayed carbon-14 nuclei today, in terms of n, is

2.607 1011 n. [1]

(iv) In a sample initially containing only radioactive carbon-14, the number of

remaining carbon-14 and number of stable nitrogen-14 produced are recorded

over time. The recording ends when there is negligible number of carbon-14

nuclides left in the sample.

Hence, sketch in the same axes on Fig. 8.3, the graphs of

1. the number of remaining carbon-14 nuclides (Graph C)

2. the number of nitrogen-14 nuclides produced (Graph N)

Label all relevant values from part (b) in the graph. [2]

Fig. 8.3

END OF PAPER

number of nuclides

time / years

27


For Examiner’s

Use BLANK PAGE

28

SRJC 2015 9646/PRELIM/2015

For Examiner’s

Use

BLANK PAGE


PHYSICS 9646

Preliminary Examination 24 Aug 2015 Paper 3 Longer Structured Questions 2 hours Candidates answer on the Question Paper. No Additional Materials are required.



Section A Answer all questions. Section B Answer any two questions. You are advised to spend about an hour on each section. At the end of the examination, fasten all your work securely together. The number of marks is given in bracket [ ] at the end of each question or part question. .

This document consists of 29 printed pages.


Q1 / 8

Q2 / 9

Q3 / 7

Q4 / 8

Q5 / 8

Q6 / 20

Q7 / 20

Q8 / 20

Total marks

/ 80

NAME

CG INDEX NO.

2

SRJC 2015 9646/MYE/2015

DATA AND FORMULAE

Data




= (1/(36 π)) x 10-9 F m-1











3


For Examiner’s

Use Formulae


v2 = u2 + 2as




-r



= 2 2

0±ω x - x


of an ideal gas,






where k = 2

2

8 ( - )m U E

h



2

1

693.0

t

4

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

Section A


1 (a) State the First Law of Thermodynamics.

…………………………………………………………………………………………………..…

…………………………………………………………………………………………………..…

……………………………………………………..…………………………………………... [1]

(b) An ideal gas is placed in an insulated cylinder as shown in Fig. 1.1.

Fig 1.1

Initially, its pressure is 1.04 x 105 Pa and its temperature is 314 K. 28.6 J of heat is then

applied to the gas, causing its volume to increase from 2.9 x 10-4 m3 to 4.0 x 10-4 m3

while keeping its pressure constant.

(i) Calculate the work done on the gas.

work done on gas = ……………………….. J [2]

(ii) Show that the change in internal energy of the gas is 17.2 J.

change in internal energy = ……………………….. J [1]

The increase in internal energy of a system is equal to the sum of the heat absorbed by the system and the work done on the system [B1].

piston

gas

Work done on gas = -p (V2 – V1) = - (1.04 x 105)(4.0 x 10-4 - 2.9 x 10-4) [M1] = - 11.4 J [A1]

ΔU = Q + W = 28.6 + (-11.4) [M1] = 17.2 J

5


For Examiner’s

Use (iii) Calculate the new temperature of the gas given that it has 6.96 × 1021

molecules.

new temperature = ……………………….. K [2]

(iv) Calculate the ratio of the final r.m.s. speed to the original r.m.s. speed of the

molecules.

ratio = ……………………….. [2]

ΔU = 3/2 NkΔT 17.2 = 3/2 (6.96 × 1021)(1.38 ×10-23) ΔT [M1] ΔT = 119 K Hence new temperature = T + ΔT = 314 + 119 = 433 K [A1]

½ m <c2> = 3/2 kT √<c2> = √(3kT/m) [M1] Since k and m are constant, Ratio = √(Tf/Ti) = √(433/314) = 1.17 [A1]

6

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

r /106 m

0 5.0 10.0 15.0 20.0 25.0

10.0

8.0

6.0

4.0

2.0

0

g /N kg−1

2 (a) Fig. 2.1 shows a graph of the variation of the gravitational field strength g of the Earth

with distance r from its centre.

Fig. 2.1

(i) State the relationship between gravitational field strength g and gravitational potential Φ.

....................................................................................................................................... [1]

(ii) Define gravitational potential energy.

……...................................................................................................................................

..........................................................................................................................................

....................................................................................................................................... [1]

(iii) Hence, estimate the work done in bringing a mass of 5.0 kg from r = 25 x 106 m to r = 10 x 106 m.

work done = ………………………….. J [3]

By estimation, area under graph = 2.2 x 107 J kg−1 [B1] (Accepted range: 2.1 x 107 – 2.5 x 107) Work done by external force = − m x area under graph

= − 5 x 2.2 x 107 [M1] = − 1.1 x 108 J [A1]

The gravitational potential energy of a mass at a point within a gravitational field is the work done by an external force to move the mass from infinity to that point [B1].

d

dr

g = - [B1]

7


For Examiner’s

Use (b) A star system consists of 3 stars X, Y and Z, each of mass 4.0 x 1022 kg, moving with

the same speed and in the same direction in a circular orbit of radius 9.8 x 1013 m about a central star P of mass 7.0 x 1024 kg. Stars X, Y and Z are always positioned at a distance 1.7 x 1014 m from each other as shown in Fig. 2.2.

Fig. 2.2

(i) By considering all the forces acting on X, show that the acceleration of X is

4.9 x 10−14 m s−2. [3]

(ii) Comment on the work done in bringing a unit mass from X to Y.

……...................................................................................................................................

..........................................................................................................................................

....................................................................................................................................... [1]

X

Z Y

P

1.7 x 1014

m

There is no change in potential from X to Y, hence zero work done [B1].

The sum of gravitational forces due to Z, Y and P provide the centripetal force for circular motion. [B1] Fnet = ma FZ+FY+FP =ma [M1] 2FZ cos 30°+ FP =ma

2

14 132 cos30

1.7 10 9.8 10

M

2 2

Gm Gmma

14 13

11 22 11 24

14 13

14 2

2 cos301.7 10 9.8 10

6.67 10 4.0 10 6.67 10 7.0 10 2 cos30 [M1]

1.7 10 9.8 10

=4.9 10

M

ms

2 2

2 2

Gm Ga =

8

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

3 A block of wood of mass 1.2 kg and cross sectional area of 80 cm2 floats in still water of density 1000 kg m−3 as shown in Fig. 3.1. The height of the portion of the block submerged in water is 15.0 cm.

Fig. 3.1

The block is then pushed down into the water through a depth of 7.0 cm. When the block is released, the block bobs up and down in water. The acceleration of the block a is given by the expression

a = − 65.4x

where x is the vertical displacement from its floating position (a) Show that the frequency of oscillation of the block is 1.29 Hz. [1]

(b) Calculate the additional upthrust when the block was pushed down from its floating position.

additional upthrust = ………………………….. N [2]

Water trough

f =

2

65.4 [M1]

2

1.29Hz

Additional upthrust = ρwgAx = 1000(9.81)(80x10−4)(7x10−2) [M1] = 5.49 N [A1]

Block of wood

9


For Examiner’s

Use (c) On Fig. 3.2, sketch a labelled graph of additional upthrust against the vertical

displacement from the block’s floating position x. [1]

Fig. 3.2

(d) Hence, calculate the total energy of the oscillation.

total energy = ………………………….. J [2]

(e) Surface water waves of speed 0.90 m s−1 are then incident on the block. These cause resonance in the up-and-down motion of the block.

Calculate the wavelength of the water waves.

wavelength = ………………………….. m [1]

For resonance, driving frequency = natural frequency of block-water system = 1.29 Hz v = fλ 0.9 = 1.29 (λ) [M1] λ = 0.698 m

Total energy of oscillation = area under graph

= 21(5.49)(7 10 )

2 [M1]

= 0.192 J [A1]

Additional upthrust / N

x / m 0 0.07

5.49

10

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

4 The Principle of Conservation of Energy can be used to calculate the stopping and

accelerating potentials in the Photoelectric Experiment and generation of X-rays respectively.

(a)(i) Using the Principle of Conservation of Energy, explain Einstein’s Photoelectric

equation: hf = + ½mvmax2

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

……………………………………………………………………………………………………………

……………………………………..………………………………………………………………... [2]

(ii) In a photoelectric experiment, the work function of a photoemissive material is 1.3 eV

and the wavelength of the light is 550 nm.

Calculate the value of the stopping potential.

potential = ……………………….. V [2]

(b)(i) Using the Principle of Conservation of Energy, derive the expression for the minimum

wavelength of the continuous X-ray spectrum in terms of the accelerating potential

between the anode and the cathode, V.

[2]

When the energy of a photon (given by hf) is absorbed, part of the energy is used to free the electron from the photoemissive material [B1] and the remaining will appear as the maximum kinetic energy of the photo-electron if there is no other energy loss (or appear as the kinetic energy of the electron at the surface which will be a maximum) [B1].

The electron gains KE and loses EPE as it accelerates between the anode and cathode, KE = eV When the electron loses all of its KE upon the 1st scattering process, an x-ray photon with the minimum wavelength is obtained,

hc/min = KE = eV [M1 for both equations]

Therefore, min = hc/eV [A1] Note: 1 mark if did not explain how the 2 equations are derived

hc/ = + eVs hc/(550 x 10-9) = 1.3 x 1.6 x 10-19 + 1.6 x 10-19 V [M1] Vs = 0.96 V [A1]

11


For Examiner’s

Use

(ii) Fig. 4.1 shows the X-ray spectrums of an X-ray tube with tungsten and barium as the anodes respectively.

Fig 4.1

1. State whether the accelerating potentials to produce the X-ray spectra for both tungsten and barium are the same or different.

……………………………………………………………………………………………….[1]

2. Calculate the accelerating potential for the tungsten spectrum.

potential = ………………………. V [1]

Using min = hc/eV 16 x 10-12 = 6.63 x 10-34 x 3 x 108 / 1.6 x 10-19 V V = 77,700 V [A1]

same

12

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

5 Fig. 5.1 shows the I-V characteristic of a semiconductor diode.

Fig. 5.1

(a) State how the resistance of the diode changes when the potential difference applied

across it:

(i) decreases from 0 V (ie. becomes more negative)

………………………………………………………………………………………………

………………………………………………………………………………………[1]

(ii) increases from Vo

………………………………………………………………………………………………

………………………………………………………………………………………[1]

(b) The semiconductor diode is made up of a p-n junction.

(i) Describe qualitatively the origin of the depletion region at a p-n junction when a

p-type semiconductor and an n-type semiconductor are brought together.

……………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

resistance increases and becomes very large / almost infinite [B1]

Vo V 0

I

Once a p-type and n-type semiconductor are brought together, due to

the difference in concentration [B1], electrons from the n-type

semiconductor close to the junction will diffuse across the junction to the

p-type semiconductor and similarly, holes from the p-type

semiconductor will diffuse to the n-type semiconductor [B1].

The electrons and holes will then readily combine, resulting in the

junction becomes depleted of mobile charge carriers [B1]. This region is

called the depletion layer.

A potential difference and hence an internal E-field quickly develops at the junction, with the n-side positive relative to the p-side. This prevents further diffusion of electrons and holes. [B1]

resistance decreases significantly to almost zero [B1].

13


For Examiner’s

Use

………………………………………………………………………………………………

………………………………………………………………………..…………………. [4]

(ii) With reference to the depletion region, explain why the resistance of the diode is

as stated in (a)(ii) when a potential difference of greater than Vo is applied across

it.

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

………………………………………………………………………………………………

……………………………………………………..……………………………………. [2]

When the potential difference applied is greater than Vo, the emf source pushes electrons in the n-side and holes in the p-side towards the junction. [B1]

The depletion layer is replenished with a fresh supply of mobile charge carriers, and therefore narrows to allow the flow of current across the junction and hence the resistance drops significantly [B1].

or

When the potential difference applied is greater than Vo, the external e-field generated by the emf source across the diode acts in the opposite direction to the internal E-field in the junction, giving rise to a resultant field that is pointing from the p-side to the n-side [B1].

The depletion layer is replenished with a fresh supply of mobile charge carriers, and therefore narrows to allow the flow of current across the junction and hence the resistance drops significantly [B1].

14

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

Section B

Answer two questions from this section.

6 (a) Describe, with a labelled diagram, an experiment to determine the speed of sound using

stationary waves.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [5]

Method 1

Labelled diagram with a signal generator, loudspeaker, CRO, microphone, reflector

[1]

A wave of known frequency is generated by a source, e.g. a loudspeaker connected

to a signal generator. [1]

Shift the microphone until it registers the highest / lowest signal [1]

The wavelength of the wave, = 2d, where d is the distance between two adjacent

nodes (or two adjacent antinodes). [1]

Using v= f to calculate the speed of sound [1]

Method 2

Labelled diagram with a tube with 2 open ends, tuning fork and a container of water

[1]

Use a tuning fork with known frequency. [1]

Shift the tube upwards until the first loud sound is heard. [1]

The wavelength of the wave, = 4L where L is the length of the tube above water

surface. [1]

Use v= f to calculate the speed of sound [1]

signal

generator

Source (e.g. loudspeaker

connected to signal

generator)

CRO

Detector (e.g.

microphone)

reflector

Tuning fork Tube

water

15


For Examiner’s

Use

(b) In Fig. 6.1 below, a string which is connected to an oscillator at one end, is held down by a weight at the other end.

(i) The frequency of the oscillator is adjusted such that a stationary wave with its

second lowest resonant frequency is formed. On Fig. 6.2 below, draw a diagram to

represent this mode of vibration. [1]

(ii) The weight is then adjusted such that the speed of the wave along the string is doubled from (b)(i), while the settings of the oscillator remain unchanged. On Fig. 6.3 below, draw a diagram to represent this mode of vibration. [1]

Method 3

Labelled diagram with a signal generator, loudspeaker, tube / pipe [1]

Slowly increase the frequency of signal generator until the first loud sound is heard.

[1]

Record of frequency of the sound from signal generator. [1]

= 2L where L is the length of the tube / pipe. [1]

Use v= f to calculate the speed of sound. [1]

If the tube / pipe is closed in one end, then = 4L

Signal generator

loudspeaker

Tube / pipe

oscillator weight

pulley


oscillator weight

pulley


Fig. 6.1

Fig. 6.2

oscillator weight

pulley


Fig. 6.3

16

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

(iii) If the speed of the wave along the string in (b)(ii) is 3.5 m s-1, and the distance between the oscillator and the pulley is 3.0 m, determine the fundamental frequency.

fundamental frequency = .................................. Hz [2]

(c) During a fireworks display, a firework explodes high in the air as shown in Fig. 6.4. Two

detectors X and Y are 450 m and 150 m respectively away from the source of the fireworks.

Assume that the sound wave spreads out uniformly in all directions and reflections from the

ground and energy losses in the air can be ignored.

The sound that reaches detector X has an intensity of 0.20 W m-2 and an amplitude of A.

(i) Determine, for detector Y,

1. the intensity of the sound detected.

intensity = .......................... W m-2 [2] 2. the amplitude of the sound detected in terms of A.

amplitude = ................ A [2]

v = fo o 3.5 = fo (3.0 x 2) [M1] fo = 0.583 Hz [A1]

X Y

450 m 150 m

fireworks

Fig. 6.4

[A1] m W 80.1

[M1] 150

450

20.0

1

2-

22

2

Y

Y

Y

X

X

Y

I

I

r

r

I

I

rI

[A1] 3

[M1] 20.0

8.122

2

AA

A

A

A

A

I

I

AI

Y

Y

X

Y

X

Y

17


For Examiner’s

Use

(ii) Determine the ratio surface area of detector X

surface area of detector Y such that both detectors receive the

same amount of power.

ratio = ……………… [2]

area surface

power Intensity . When the power is the same,

area surface

1 Intensity [B1]

As 9X

Y

I

I, for the same power, 9

area surface

area surface

Y

X [B1]

18

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

(d) In a simple experiment to find out the wavelength of monochromatic red light emitted by a laser,

a fine beam of red laser light is shone through a diffraction grating as shown below in Fig 6.5.

The diffraction grating has 300 000 lines per metre and is set so that its plane is normal to the

incident light. Bright spots of first and second orders are observed at 0.46 m and 1.00 m

respectively, from the central spot on a screen which is 2.00 m from the grating.

(i) From the first-order diffracted light, estimate the wavelength of the laser light.

wavelength = ……………………….. m [3]

(ii) State and explain an advantage of obtaining the wavelength of the laser light by using the second-order diffracted light rather than the first-order diffracted light.

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………………………………………………………………………………………………

……………..………………..…………………………………………………….………… [2]

Fig 6.5

laser

grating

2.00 m

0.46 m

1.00 m

Diffraction angle of first order maximum

θ = tan-1

(0.46/2.00) = 12.95 o

[M1]

From d sin θ = nλ, where d = (1 / 300 x 103)

m-1

and n = 1:

λ110300

12.95 sin3

[M1]

λ = 7.47 x 10-7

m [A1]

The wavelength can be more precisely determined. [A1] The larger angle of diffraction can be measured experimentally with a lower percentage error with a measuring instrument of a certain precision [M1].

19


For Examiner’s

Use 7 (a) (i) Define electric field strength.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………..………………………………... [1]

(ii) Define electric potential.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

…………………………………………………………..………………………………... [1]

Electric field strength at a point in an electric field is the electric force per unit positive charge acting on a small stationary test charge placed at that point [B1].

Electric potential at a point in an electric field is the work done by an external force in moving a point charge from infinity to that point (without a change in its kinetic energy). [B1].

20

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

(b) Two charged solid metal spheres A and B are situated in a vacuum. Their centres are

separated by a distance of 12.0 cm, as illustrated in Fig. 7.1. The diagram is not to

scale.

Point P is a point on the line joining the centres of the two spheres. Point P is a

distance x from the centre of sphere A.

The variation with distance x of the electric field strength E at point P is shown in Fig.

7.2. A positive value of E on the graph at a point corresponds to an electric field vector

pointing horizontally to the right.

Fig. 6.1

21


For Examiner’s

Use

(i) State and explain:

1. the signs of charges of A and B.

……………………………………………………………………………………………

……………………………………………………………………………………………

…………….…………………………………………………………………………….[2]

2. the ratio of the radius of sphere A to that of sphere B.

………………………………………………………………………………………….…

………………………………………………………………………………………….…

…………….………………………………………………………………..…………. [2]

3. how the electric potential varies inside spheres A and B.

……………………………………………………………………………………………

……………………………………………………………………………………………

…………….…………………………………………………………………………... [2]

(ii) A student is interested to find out how the electric potential changes for different

locations of point P.

1. It is given that the ratio of the charges of spheres A and B respectively is

numerically 4:1. If the electric field strength when x = 4.0 cm is 1.25 × 107 N C-1,

calculate the numerical values of the charges of spheres A and B respectively.

charge of sphere A = ………………………. C

charge of sphere B = ………………………. C [3]

A and B are both positively charged [M1] because the electric field lines point to the right away from sphere A and to the left away from sphere B, and electric field lines point away from positive charges. [A1].

7:3 [B1], as the electric field strength is zero within each sphere [B1].

Electric potential is constant inside each sphere [M1], as zero electric field strength within a sphere implies zero potential gradient [A1].

QA = 4QB <1> At 4 cm, EA – EB = 1.25 × 107

QA/[4o(0.04)2] – QB/[4o(0.08)2] = 1.25 × 107 [M1] Substituting <1>,

4QB/[4o(0.04)2] – QB/[4o(0.08)2] = 1.25 × 107

Solving, QB = 5.93 × 10-7 C [A1]

QA = 2.37 × 10-6 C [A1]

22

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

2. Hence, show that the electric potential at the point P when x = 8.0 cm is

4.0 x 105 V. [1]

3. Using (i) 2, (i) 3 and (ii) 2, sketch the graph of electric potential energy of an

electron against x, labelling the electric potential energy at point P where

x = 8.0 cm. The numerical values of electric potential energy of the electron

when it is at the surfaces of both spheres are not required. [3]

EPE / J

x / cm

1.4 8.0 11.4 12.0

-6.4 x 10-14

[B1] Maximum point at 8.0 cm with value ofEPE labelled. [B1] Constant EPE within spheres (1.4 and 11.4 cm labelled) [B1] Lower EPE within sphere A than B.

V = QA/[4o(0.08)] + QB/[4o(0.04)]

= (2.37 × 10-6)/[4o(0.08)] + (5.93 × 10-7)/[4o(0.04)] [M1] = 4.00 × 105 V

23


For Examiner’s

Use

(iii) The student places an electron at x = 10.0 cm and releases it.

1. State and explain which sphere the electron will move towards.

……………………………………………………………………………………………

……………………………………………………………………………………………

…………….…………………………………………………………………………... [1]

2. Describe and explain the respective changes to the electron’s kinetic

energy and electric potential energy.

……………………………………………………………………………………………

……………………………………………………………………………………………

……………………………………………………………………..…………………..…

……………………………………………………………………..…………………...[2]

3. Hence or otherwise, calculate the final speed of the electron just before it

hits the sphere as stated in (iii) 1. The electric potential at x = 10.0 cm is

4.8 x 1019 V, while the electric potentials at the surfaces of spheres A and B

are 1.6 x 1020 V and 1.1 x 1020 V respectively.

speed = ………………………. m s-1 [2]

As it experiences a force, it accelerates and its KE increases [B1]. By Principle of Conservation of Energy, its EPE decreases [B1].

Sphere B, as the direction of the net electric field is to the left, so it will experience a force to the right [B1].

By PCOE, Gain in KE = Loss in EPE ½ me v

2 = q (V10 – VB) ½ (9.11 x 10-31) v2 = (-1.6 x 10-19) (4.8 x 1019 - 1.1 x 1020) [M1] v = 4.67 x 1015 ms-1 [A1]

24

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

8 (a) The binding energy per nucleon of a cobalt-60 ( Co2760 ) nuclide is 8.74 MeV. Some rest

mass information is also shown below.

Rest mass of a neutron = 1.008665 u

Rest mass of a proton = 1.007825 u

Rest mass of an electron = 0.000549 u

(i) Calculate, to 5 decimal places, the rest mass of cobalt-60 in terms of u.

rest mass = …………………… u [3]

Fig. 8.1 shows the process of decay where Cobalt-60 undergoes nuclear decay to form

the stable isotope nickel-60. In the process of decay, Cobalt-60 emits one beta particle

with an energy of 310 keV and then two gamma rays with energies of 1.17 MeV and

1.33 MeV respectively.

Fig. 8.1

60

27Co

310 keV ()

1.17 MeV ()

1.33 MeV ()

60Ni

Binding energy of Co = 8.74(106)(1.6 × 10−19)(60)

𝐵𝑖𝑛𝑑𝑖𝑛𝑔 𝑒𝑛𝑒𝑟𝑔𝑦 = ∆𝑚 𝑐2 = (∑ 𝑚 − 𝑀𝐶𝑂) 𝑐2

𝑀𝐶𝑂 = (33 × 1.008665𝑢 + 27 × 1.007825𝑢) −8.3904 × 10−11

(3 × 108)2 (1.66 × 10−27)𝑢 [𝑀1]

= 8.3904 × 10−11 J [M1]

= 59.93561𝑢 [𝐴1]

25


For Examiner’s

Use (ii) Write down the number of protons and neutrons in the nickel nuclide produced

when the cobalt-60 nuclide decays.

number of protons = ……………………

number of neutrons = ……………………. [1]

(iii) By considering the rest mass of the energy components (beta particle and

gamma rays), calculate, to 5 decimal places, the rest mass of the stable nickel

nuclide in terms of u.

rest mass = …………………… u [3]

(iv) In practice, the above radioactive decay of cobalt-60 could be used for the

treatment of cancer.

Suggest and explain which type of radiation of the decay is used for the purpose

of tumour treatment.

………………………………………………………………………………………

…………………………………………………………………………………...[2]

28

32

The gamma radiation [M1] emitted from the process is used to treat the cancer cells as it has a very high penetrative power [A1].

[𝑚]𝑒𝑛𝑒𝑟𝑔𝑦 = (0.31 + 1.17 + 1.33)(106)(1.6 × 10−19)

(3 × 108)2 (1.66 × 10−27)𝑢 = 3.00937 × 10−3𝑢 [𝑀1]

Considering the rest mass of energy components,

[𝑚𝑐2]𝑒𝑛𝑒𝑟𝑔𝑦 = (0.31 + 1.17 + 1.33)(106)(1.6 × 10−19) J

Rest mass of nickel = Mco melectron [m]energy

= 59.93561u 0.000549u 0.00300937u [M1] = 59.93205u [A1]

26

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

(v) 1. Sketch a graph to show the variation of binding energy per nucleon with

nucleon number, and mark the binding energy per nucleon of a cobalt-60

nuclide on the graph. [2]

nucleon number


nucleon number


8.74

(56) (56 - not marking pt)

60

Shape [B1] Labelled axes (relative position of Cobalt-60) [B1]

27


For Examiner’s

Use 2. Hence, state and explain the nuclear process a nuclide of nucleon number

120 will most likely undergo.

………………………………………………………………………………………

……………………………………………………………………………………...

…………………………………………………………………………………... [2]

(b) A carbon-14 14

6C nuclide undergoes spontaneous and random beta decay to

transform into a stable nitrogen-14 14

7N nuclide.

14 14 0

6 7 -1C N+ β

(i) Explain the terms spontaneous and random.

………………………………………………………………………………………

……………………………………………………………………………………...

…………………………………………………………………………………...[2]

(ii) The nuclide of carbon-14 has a half-life of 5730 years. If a carbon-14 source

emits n β-particles in one second today, calculate the time taken for the source to

emit the same number of beta particles 10,000 years later.

time taken = ………………. s [2]

Spontaneous - Not affected by physical conditions e.g. temperature, pressure,

electric and magnetic fields etc. [B1]

Random - Impossible to predict exactly when a particular nucleus will decay.

However, there is a constant probability of decay of an individual nucleus per unit

time. [B1]

[M1] s 298.0

2

1

2

1

1-

5730

10000

,5.0

nA

n

A

A

A Ct

t

o

10,000 years later, source emits 0.298n -particles in 1 s.

Time taken to emit n -particles = s 35.3298.0

n

n [A1]

A fission reaction [A1] would result in the product having higher binding energy

per nucleon, thus more stable. [M1]

28

SRJC 2015 9646/MYE/2015

For Examiner’s

Use

(iii) Show that the number of undecayed carbon-14 nuclei today, in terms of n, is

2.607 1011 n. [1]

(iv) In a sample initially containing only radioactive carbon-14, the number of

remaining carbon-14 and number of stable nitrogen-14 produced are recorded

over time. The recording ends when there is negligible number of carbon-14

nuclides left in the sample.

Hence, sketch in the same axes below, the graphs of

1. the number of remaining carbon-14 nuclides (Graph C)

2. the number of nitrogen-14 nuclides produced (Graph N)

Label all relevant values from part (b) in the graph. [2]

number of nuclides

time / years

n

nAN

NA

O

O

11

O

O

10607.2

)606024365(5730

2ln

[M1]

29


For Examiner’s

Use

END OF PAPER

number of nuclides

time / years

N

C

5730

Shape of both graphs – [B1] Labeling of half-life and No/2– [B1]

1.304 x 10 11 n

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PHYSICS 9646 - Weeblyscore-in-chemistry.weebly.com/uploads/4/8/7/1/48719755/srjc_2015...PHYSICS 9646 Preliminary ... For each question there are four possible ... = 1.67 x 10 27 kg