IIT Jam 2016 Physics Solutions

7/25/2019 IIT Jam 2016 Physics Solutions

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NIIT JAM-2016 PHYSICS-SOLUTIONS

1. For an infinitely long wire with uniform line charge density, , along thez-axis, the electric field at apoint (a,b, 0) away from the origin is

( ,

ye e

and ze are unit vectors in Cartesian-Coordinate system.)

(a) 2 20

( )2

x ye ea b

(b) 2 20 ( )

2 x yae be

a b

(c) 2 20

2

xe

a b

(d) 2 2

0

2

ze

a b

Ans. (b)

y

( , ,0)a b

r

e

x

E= 2

re

r

r= 2 2a b

re = 2 2

x y

ae ber

r a b

E

= 2 2 ( )2 ( ) x yae be

a b

2. A 1W point source at origin emits light uniformly in all the directions. If the units for both the axes are

measured in centimetre, then the Poynting vector at the point (1, 1, 0) in W/cm2is

(a)1

( )8 2

x ye e

(b)1

( )16

x ye e

(c)1

( )16 2

x ye e

(d)1

( )4 2

x ye e

Ans. (a)

S

= 2 4 r

Pe

r

r= 2

re =

2

x ye e


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NS

= ( )1

4 2 2

x ye e

=1

( )8 2

x ye e

3. A charged particle in a uniform magnetic field0 z

B B e

starts moving from the origin with velocity

(3 2 ) m / s.x zv e e The trajectory of the particle and the timetat which it reaches 2 meters above the

xy-plane are

( ,x ye e and ze are unit vectors in Cartesian-Coordinate system.)

(a) Helical path;t= 1s (b) Helical path;t= 2/3s

(c) Circular path;t= 1s (d) Circular path;t= 2/3s

Ans. (a)

Its velocity component inz-direction is 2m/s. Its path will be helical and will reach 2mabovexyplane

is 1 sec.

4. Consider the particle mass mfollowing a trajectory given0 1cosx x t and 0 2siny y t where

0 0 1, ,x y and 2 are constant of appropriate dimensions. The force on the particle is(a) central only if

1 2 (b) central only ifx0= y0and 1 2

(c) always central (d) central only if x0=y0and 1 2 Ans. (a)

r =

1 2 cos sinx ti y tj

a

=

22 2

1 1 2 22 cos sin

d rx ti y tj

dt

If1 2 then a

= 21 r

F

= 21

ma m r

which will be central

5. Which one of the following points represent the complex number =1

?1 i

(a)

1 0.5 0.5 1

0.5

1

0.5

1

y

x

(b)

1 0.5 0.5 1

0.5

1

0.5

1

y

x

(c)

1 0.5 0.5 1

0.5

1

0.5

1

y

x

(d)

1 0.5 0.5 1

0.5

1

0.5

1

y

x


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NAns. (a)

z=1 (1 ) 1 1 1

1 (1 )(1 ) 2 2 2

i ii

i i i

1 0.5 0.5 1

0.5

1

0.5

1

y

x

6. The eigenvalues of the matrix representing the following pair of linear equationsx+iy= 0,ix+y= 0

are

(a) 1 +i, 1 +i (b) 1 i, 1 i

(c) 1,i (d) 1 +i, 1 i

Ans. (d)

x+iy=0

ix+y=01

1

i x

i y

=0

0

let1 & 2 are eigenvalues

1 2 =2

1 2 =2

1 = 21 , 1i i

7. The solution of the Boolean equationY A B AB is(a) 1 (b) AB

(c) AB (d) A BAns. (d)

Y=A B AB =A B A B

= ( 1)A B B

=A B8. A spherical closed container with smooth inner wall contains a monoatomic ideal gas. If the collisions

between the wall and the atoms are elastic, then the Maxwell speed distribution function vdn

dv

for

the atoms is best represented by :

(a)

vdn

dv

v0

(b)

vdn

dv

v0


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N(c)

vdn

dv

v0

(d)

vdn

dv

v0

Ans. (c)

9. Two sinusoidal signals of frequenciesx and y having same amplitude are applied to x- and y-

channels of a cathode ray oscilloscope (CRO) respectively. The following stationary figure will be

observed wheny1

1

x1 1

(a) y x (b) Phase difference is 0

(c) 2y x (d) phase difference is / 2.Ans. (b)

y

x

=

No. of timesfig. cuts axis

No. of timesfig. cuts axis

x

y

n x

n y

=2 1

4 2

x =2

y

Phase difference = 0 or .

10. The phase difference ( ) between input and output voltage for the following circuits (i) and (ii)

vi

C

C vi Cvo vo

R

~ ~

(i) (ii)

will be

(a) 0 and 0 (b) / 2 and 0 / 2 respectively

(c) / 2 and / 2 (d) 0 and 0 / 2 respectivelyAns. (d)


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N(i) Vi =

i tV e

Z=1 1 2

j C j C j C

V =1

2

j tVi ej C

phase diff. =0

(ii) Z= 22 2

1 1 iR R ej C C

1 1tanCR

i=

( )

2

2 2

1

j t

iV V e

ZR

C

V =2

2

2 2

1

1

j t

V ei

j CR

C

0

2

11. For the given set of equations :x+y= 1,x+z= 1,x+z= 1, which one of the following statements is

correct?

(a) Equations are inconsistent

(b) Equations are consistent and a single non-trivial solution exist.

(c) Equations are consistent and many solution exist.

(d) Equations are consistent and only a trivial solution exist

Ans. (b)

x+y=1

y+z=1x+z=1

1 1 0

0 1 1

1 0 1

x

y

z

=

1

1

1

1 1 0 1 1 0 1 1 0

0 1 1 ~ 0 1 1 ~ 0 1 1

1 0 1 0 1 1 0 0 2

rank = 3. So, it will have unique solution.

12. The tangent line to the curvex2+xy+ 5 = 0 at (1, 1) is represented by(a) y= 3x 2 (b) y= 3x+ 4

(c) x= 3y 2 (d) x= 3y+ 4

Ans. (b)

x2+xy+ 5=0

Taking derivative

2 dy

x x ydx

=0


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NAt (1, 1) 3

dy

dx

y=3x+C

It passes through (1, 1)

y=3x+ 4

13. In the following RC circuit, the capacitor was charged in two different ways.

(i) The capacitor was first charged to 5V by moving the toggle switch to position P and then it was

charged to 10V by moving the toggle switch to position Q

(ii) The capacitor was directly charged to 10 V, by keeping the toggle switch at position Q

Assuming the capacitor to be ideal, which one of the following statement is correct?

R

P

Q

10V

5V

C

(a) The energy dissipation in cases (i) and (ii) will be equal and non-zero

(b) The energy dissipation for case (i) will be more than that for case (ii)

(c) The energy dissipation for case (i) will be less than that for case (ii)

(d) The energy will not be dissipated in either case.

Ans. (c)

Similar problem is Samvedna Book.14. If a constant voltage +Vis applied to the input of the following OPAMP circuit for a timet, then the

output voltageVwill approach

C

V0

R

+V

+

(a) +Vexponentially (b) Vexponentially(c) +Vlinearly (d) Vlinearly

Ans. (d)

It is integrator circuit

15. In the followingRCnetwork, for an input signal frequency1

,2

fRC

the voltage gaino

i

v

v and the

phase angle betweenvoandvirespectively are


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Nvi

C

vo

R

~

C

R

(a)1

2and 0 (d)

1

3and 0

(c)1

2and

2

(d)

1

3and

2

Ans. (b)

Let Vi = i tV e

z=

1

1

1

Rj C

Rj C

Rj C

=1

j RR

C j CR

f=1 1 1

22

f CRC RC R

Z=1

RR jR

j

=(1 )

2

j RR jR

=4 /43 3 3 3 3(1 ) 2

2 2 2 2 2

j iR RR j R j e e

i= 42

3

i ti

V Ve

z R

V

=1

R

j R

i=( /4)2

1 3

j tR V ej R

=( /4)

/4

2

33 2

j t j t

j

V Ve e

e

i

V

V

=1

, 03


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N16. Light travelling between two points takes a path for which

(a) time of flight is always minimum (b) distance is always minimum

(c) time of flight is extremum (d) distance is extremum

Ans. (a)

17. Consider a free electron (e) and a photon (ph) both having 10eVof energy. If and prepresentwavelength and momentum respectively, then

(mass of electron = 9.1 1031

kg; speed of light = 3 108

m/s)(a) e ph andPe=Pph (b) e ph andPe>Pph

(c) e ph andPe


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NAns. (a)

For isobaric process

dS= pC dTdQ

T T

S=CplogT+C1

T=

1

p

S C

Ce

For Isochoric process

dS= VC dTdQ

T T

S=CVlogT+C2

T=

2S C

Ce

19. If U, F, H, and G represent internal energy, Helmholtz free energy, enthalpy, and Gibbs free energy

respectively, then which one of the following is a correct thermodynamic relation?

(a) dU=PdVTdS (b) dH=VdP+TdS

(c) dF= PdV+SdT (d) dG=VdP+SdTAns. (b)

dU=TdSPdV

H=U + PV

dH=dU + PdV + VdP

=TdS pdV + PdV + VdP

=TdS+VdP

20. A train passes through a station with a constant speed. A stationary observer at the station at platform

measure the tone of the train whistle as 484 Hz when it approaches the station and 442 Hz when it

leaves the station. If the sound velocity in air is 330 m/s, then the tone of the whistle and the speed of

the train are

(a) 462 Hz, 54 km/h (b) 463 Hz, 52 km/h(c) 463 Hz, 56 km/h (d) 464 Hz, 52 km/h

Ans. (a)

Let speed of train isVwhen train approaches the station

f1 =484

Vf

V V

whereV= 330m/s

when train leaves the station f2 = 442 V

fV V

So,484

f= 1

V V V

V V

...(1)

&442

f= 1

V V V

V V

...(2)

(1) + (2) 1 1

484 442f

=2

f =462 Hz


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NPuttingfin (2)

V=14.93m/s

=14.93

3600 53.75 /1000

km s

21. The minimum length of a plane mirror to the see the entire full length image of an object is half of the

objects height. Suppose is the distance between eye and top of the head of the person of heighth.

The person will be able to see his entire full length image with a mirror of heighth/2 fixed on the wall(a) when the bottom edge of mirror is kepth/2 above the floor

(b) when the bottom edge of mirror is kept ( ) / 2h above the floor

(c) when the bottom edge of mirror is kept ( ) / 2h above the floor(d) when the centre of the mirror is at the same height as centre of the person

Ans. (c)

h-

h-2

22. A particle is moving in a plane with a constant radial velocity of 12 m/s and constant angular velocity

of 2 rad/s. When the particle is at a distancer= 8 m from the origin, the magnitude of the intantaneous

velocity of the particle in m/s is

(a) 8 15 (b) 20

(c) 2 37 (d) 10Ans. (b)

V

= r

re r e

= 12 16re e

| |V

= 2 212 16 20 /m s

23. A cylindrical rod of lengthLhas a mass density distribution given by 0( ) 1 ,x

xL

wherexis

measured from one end of the rod and0 is a constant of appropriate dimensions. The centre of mass

of the rod is

(a)5

9L (b)

4

9L

(c)1

9L (d)

1

2L

Ans. (a)

xcm =xdm x dx

dm dx


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N= 0

0

. 1

. 1

L

L

xx dx

L

xdx

L

=

2 3

0

3

0

52 3.

9

2

L

L

x x

LL

xx

L

24. A particle travels in a medium along a horizontal linear path. The initial velocity of the particle isv0and the viscous force acting on it is proportional to its instantaneous velocity. In the absence of any

other forces, which one of the following figures correctly represents the velocity of the particle as a

function of time?

(a)

v t( )

t

(b)

v t( )

t

(c)

v t( )

t

(d)

v t( )

t

Ans. (d)

dvm

dt=kv

dv

v=

kdt

m

v= /kt mV e

25. A lightly damped harmonic oscillator with natural frequency0 is driven by a periodic force of

frequency . The amplitude of oscillation is maximum when

(a) is slightly lower than 0 (b) 0

(c) is slightly higher than 0 (d) the force is in phase with the displacementAns. (a)

Amplitude maximum takes place at

2 22r

26. A block of mass 0.38 kg is kept at rest on a frictionless surface and attached to a wall with a spring of

negligible mass. A bullet weighing 0.02 kg moving with a speed of 200 m/s hits the block at time

t= 0 and gets stuck to it. The displacement of the block (in metre) with respect to the equilibrium

(Spring constant = 640 N/m)


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N(a) 2sin5t (b) cos10t(c) 0.4cos25t (d) 0.25sin40t

Ans. (d)Let instantaneous velocity imparted to the block isvApplying conservation of linear momentum

0.02200= (0.385 + 0.01)v

v=4

10 /0.4

m s

velocity, v= 10cos t

=640

400.4

k

m

x vdt =10

sin t=0.25 sin40t

27. One mole of an ideal gas with average molecular speedv0is kept in a container of fixed volume. If the

temperature of the gas is increased such that the average speed get doubled, then

(a) the mean free path of the gas molecule will increase

(b) the mean free path of the gas molecule will not change

(c) the mean free path of the gas molecule will decrease

(d) the collision frequency of the gas molecule with wall of the container remains unchanged

Ans. (b)

28. An arbitrarily shaped conductor encloses a charge q and is surrounded by a conducting hollow sphere

as shown in the figure. Four different regions of space, 1, 2, 3, and 4, are indicated in the figure.

Which one of the following statement is correct?

q

4

2

1

(a) The electric field lines in region 2 are not affected by the position of the chargeq

(b) The surface charge density on the inner wall of the hollow sphere is uniform

(c) The surface charge density on the outer surface of the sphere is always uniform irrespective of

the position of chargeqin region 1.

(d) The electric field in region 2 has a radial symmetry

Ans. (c)29. Consider a small bar magnet undergoing simple harmonic motion (SHM) along the x-axis. A coil

whose plane is perpendicular to thex-axis is placed such that the magnet passes in and out of it during

its motion. Which one of the following statements is correct? Neglect damping effects.

(a) Induced e.m.f. is minimum when the centre of the bar magnet crosses the coil

(b) The frequency of the induced current in the coil is half of the frequency of the SHM

(c) Induced e.m.f. in the coil will not change with the velocity of the magnet

(d) The sign of the e.m.f. depends on the ple (NorS) face of the magnet which enters into the coil.

Ans. (a)


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N30. An incompressible non-viscous fluid is injected into a conical pipe at it orifice as schematically shown

in the figure. The pressure at the orifice of areaA0isP0. Neglecting the effect of gravity and assuming

streamline flow, which one of the following plots correctly predicts the pressure along axis of the

cone?

/4 x^

(a)

x0x

p0

p (b)

x0x

p0

p

(c)

x0x

p0

p (d)

x0x

p0

p

Ans. (a)

Applying equation of continuity

x

V

AV =2( )x V

V= 2AV

x

Applying Bernoulli equation

21

2P V =

21

2P V

P=

22

2 4

11

2

AP V

x

31. Consider a spherical dielectric material of radius a centered at origin. If the polarization vector

0 xP P e

whereP0is a constant of appropriate dimensions, then

( ,x ye e and ze are unit vectors in Cartesian-coordinate system)


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N(a) the bound volume charge density is zero

(b) the bound surface charge density is zero at (0, 0,a)

(c) the electric field is zero inside the dielectric

(d) the sign of the surface charge density charge over the surface

Ans. (a,b,d)

At (0,0,a),

P2nP1n = bP2n =0

x

y

z

So,b =0

b = 0dP

Pdx

b =0

32. For an electric dipole with moment0 z

P P e

placed at the origin, (p0is a constant of appropriate

dimensions and ,x ye e and ze are unit vectors in Cartesian coordinate system)

(a) potential fall as 21

,r

whereris the distance from origin.

(b) a spherical surface centered at origin is an equipotential surface(c) electric flux through a spherical surface enclosing the origin is zero

(d) radial component ofE

is zero of thexy-plane

Ans. (a,c,d)

V=2

cos

4

p

r

x

y

z

33. Three infinitely long conductors carrying currentI1,I2andI3lies perpendicular to the plane of the

paper as shown below :


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NC3

C2

C1

I1

I2I3

If the value of the integral .C

B dl

for the loops,C1,C2andC3are 0 02 ,4 and 0 in the units of

N/Arespectively, then(a) I1= 3Ainto the paper (b) I2= 5Aout of the paper(c) I3= 0 (d) I3= 1Aout of the paper

Ans. (a,b)

1C

B dl

=2

I1 +I2 =2 ...(1)

B dl

=4

I2 +I3 =4 ...(2)B dl

=

I1 +I2 +I3 =1 ...(3)From (1), (2), & (3)

I3= 1 i.e. 1A into the paper

I1= 3 i.e. 3A into the paper

I2= 5A i.e. 5A out of the paper

34. In the optical arrangement as shown below, the axes of two polarizing sheetsPandQare orientedsuch that no light is detected. Now when a third polarizing sheet (R) is placed in betweenPandQ,then light is detected. Which of the following statement(s) is/are true?

P Q

detector

(a) Polarization axes ofPandQare perpendicular to each other(b) Polarization axes ofRis not parallel toP.(c) Polarization axes ofRis not parallel toQ(d) Polarization axes ofPandQare parallel to each other

Ans. (a, b, c)35. The P-V diagram below shows three possible paths for an ideal gas to reach the final stateffrom an

initial statei. Which among the following statement(s) is/are correct?

V

P

i

1

2

3

f

(a) The work done by the gas is maximum along path 3

(b) Minimum change in the internal energy occurs along path 2


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N(c) Maximum heat transfer is for path-1

(d) Heat transfer is path independent

Ans. (a)

36. Potential energyUas a function ofris shown below. If a particle of massm1and energyE1, starting

fromr>>a, moves towards the origin, then

0

U r( )

Umin

b a

c

r

m1

E1

(a) there is only one turning point for the particle

(b) velocity of the particle starts to increasex=aand reaches its maximum atr=c.(c) velocity of the particle atr=aandr=bare equal(d) the particle gets bounded if it elastically collides with a stationary particle of massm2atr=c,

imparting a momentum greater than2 12m E

Ans. (a,b,c,d)Ifm1collides with particle of massm2atr=c

Let1E is is energy of particlem1after collision

conserving energy.

10 E =2

1

22

pE

m

The particle ofm1will get bounded if

1E


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N38. Apnjunction was formed with a heavily doped (1018cm3)p-region and lightly doped (1014cm3) n-

region. Which of the following statement(s) is(are) correct?

(a) The width of the depletion layer will be more in then-side of the junction

(b) The width of the depletion layer will be more in thep-side of the junction

(c) The width of the depletion layer will be same on both side of the junction

(d) If thepnjunction is reverse biased, then the width of the depletion region increases.

Ans. (b)39. A slit has width d along thex-direction. If a beam of electrons, accelerated in y-direction to a particular

velocity by applying a potential difference of 100 0.1kV passes through the slit, then, which of thefollowing statement(s) is/are correct?(a) The uncertainty in the position of electrons in x-direction before passing the slit is zero(b) The momentum of electrons inx-direction is~h/dimmediately after passing the slit(c) The uncertainty in the position of electron iny-direction before passing the slit is zero(d) The presence of the slit does not affect the uncertainty in momentum of electrons iny-direction

Ans. (b,c,d)40. A free particle of energyEcollides with a one-dimensional square potential barrier of height V and

widthW. Which one of the following statement (s) is/are correct?(a) For E>V, the transmission coefficient for the particle across the barrier will always be unity.(b) For E


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N43. A rectangular area (A1) is formed by two vectors x

and y

as shown in figure (i). A new set of vectors,

representing the area (A2) as shown in figure (ii), are given as : 1 2; ,u x u kx y

wherek is a

dimensionless constant.

x

y 2u

1u

( )i ( )ii

The Jacobian of the frame1 2( , )u u

with respect to ( , )x y

is ___________.

Solution :

1 2,

,

u u

x y

=

1 1

2 2

1 01

1

u u

x y

u u k

x y

Ans. 1

44. A particle radioisotope has a half-life of 5 days. In 15 days the probability of decay in percentage will

be ___________.

Solution :

N= tN e

dN= tN e dtProbability of decay indttime

dN

N= te dt

Probability of decay in 15 days15

0

te dt =2 15ln

155

0 0

tte e

=1 e3 log 2

=1 7

18 8

In percentage, probability of decay is700

87.5%8

Ans. 87.5

45. In a photoelectric experiment both sodium (work function = 2.3 eV) and tungsten (work function =

4.5eV) metals were illuminated by an ultraviolet light of same wavelength. If the stopping potential

for tungsten is measured to be 1.8V, the value of the stopping potential for sodium will be ________V.

Solution :

Let stopping potential ofNaisVS

hc

=2.3eV+eVS= 4.5eV+ 1.8eV

eVS=4eV

VS=4V Ans. 4


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N46. The addition of two binary numbers 1000.01 and 0001.11 in binary representing is _________.

Solution :

1000.01

0001.11

1010.00Ans. 1010

47. The number of second nearest neighbour ions to aNa

+

ion inNaClcrystal is __________.Solution :

12 Ans. 12

48. The output voltageV0of theOPAMPcircuit given below is _______V.

V0

R

+

2R

RR

R

1V

2V

3V

Solution :

49. A cylinder contains 16 g ofO2. The work done when the gas is compressed to 75% of the original

volume at constant temperature of 27C is ___________J.

Solution :

W= 2

1

logV

nRTV

= 0.5 8.31 300 log4

=358.6 J Ans. 358.6J

50. When sunlight is focused on a paper using a bi-convex lens, it starts to burn in the shortest time if thelens is kept 0.5 m above it. If the radius of curvature of the lens is 0.75 m then, the refractive index of

the material is _________.

Solution :f= 0.5m

1

f=

1 1

1 12 1

R R

R1 =R,R2= R

2 12

R

1=2 0.75

2

=1.75 Ans. 1.75

51. Consider a closed triangular contour traversed in counter-clockwise direction, as shown in the figure

below.

The value of the integral, .F dl

evaluated along this contour, for a vector field, ,x yF ye xe

is

__________.

( ,x ye e and ze are unit vectors in Cartesian-coordinate system.)


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Ny

xO P(2. 0)

Q

4

4

Solution :

Mdx Ndy =N M

dx dyx y

ydx xdy = 2dxdy

=1

2 2 2sin2 4

= 2 2 Ans. 2 2

52. A hemispherical shell is placed on the xy-plane centered at the origin. For a vector field2 2 ( ) / ( ),

x yE ye xe x y

the value of the integral ( )S

E da

over the hemispherical surface is

___________ .Solution :

x

y

z

C

On the bounding curve of hemisphere

E

= 2 2 2

sin cosyi xj a i a j

x y a

=1

ea

Using Stokess theorem

S

E n dS

=1 1

E dr e dr dSa a

=

2

0

12a d

a

Ans. 253. The shape of a dielectric lamina is defined by the two curvesy= 0 andy= 1 x2. If the charge density

of the lamina 215 / ,yC m then the total charge on the lamina is ___________C.

Solution :


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Ny

x

y x= 1 2

q= dS

=

21 1

1 0

15x

ydy dx

=

211 122

2

1 10

1515 1

2 2

x

ydx x dx

=1 2

15 1 85 3

Ans. 8

54. In the circuit given below, the collector to emitter voltageVCEis __________V.

(NeglectVBE, take 100 )

5k

5k5k

10k

VCE

V VCC= +10

Solution :

5k

5k

10k

V VCC= +10


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NVth =

2

1 2

5CCR V

VR R

Rth =1 2

1 2

5R R

kR R

VthIBRthVBEIERE=0

IB = 5 0.7 0.0042 mA

1 5 101 10th BE

th E

V V

R R

IC= 0.42 mABI VCE=VCCIC(RC+RE)

=10 15 0.42 = 3.7 V Ans. 3.7

55. The de Broglie wavelength of a relativistic electron having 1 MeV of energy is ___________ 1012

m. (Take the rest mass energy of the electron to be 0.5MeV. Planck constant = 6.63 1034Js, Speed of

light 3 108m/s, Electronic charge = 1.6 1019C)

Solution :

E2 =m2c2+p2c2

1=0.25 +p2c2

p= 0.75 MeV/c

=

13

8

0.866 1.6 10

3 10

=4.619 1022

=34

22

6.63 10

4.619 10

h

p

=1.4354 1012m Ans. 1.4354

56. X-ray diffraction of a cubic crystal gives an intensity maximum for Bragg angle of 20 corresponding

to the (110) plane. The lattice parameter of the crystal is _____________nm.

(Consider wavelength ofX-ray = 0.15 nm)Solution :

2 sinhkld =n

2dhklsin 20 =0.15 1 (n= 1)

dhkl=0.15

0.25 nm2sin20

2 2 2

a

h k l =0.22

a= 0.22 2 0.31 nm Ans. 0.3157. X-rays of 20 keV energy is scattered inelastically from a carbon target. The kinetic energy transferred

to the recoiling electron by photons scattered at 90 with respect to the incident beam is _________keV.

(Planck constant = 6.6 1034 Js, Speed of light = 3 108m/s, electron mass = 9.1 1031 kg,

Electronic charge = 1.6 1019 C)

Solution :

KEtransferred,

KE=hc hc


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N = 1 cos

h

mc

=2.246 pm

=1240

eV nm20000

=0.062 nm

= 0.062 0.02426 0.0863 nm

hc

=

124014368.48 eV

0.0863

=14.37 KeV

KE tranfered=hc hc

=20 14.37

=5.63 KeV Ans. 5.63

58. An aluminum plate of mass 0.1 kg at 95C is immersed in 0.5 litre of water at 20C kept inside an

insulating container and is then removed. If the temperature of the water is found to be 23C, then the

temperature of the aluminium plate is __________C.(The specific heat of water and aluminum are 4200 J/kg-K and 900 J/kg-K respectively, the density of

water is 1000 kg/m3)

Solution :

Heat gained by water

Q1 =m S T =0.5 103 1000 4200 3

=6300 J

Heat lost by aluminium

=Q1= 6300 J

6300=mS T

= 0.1 900 T T =70C

Temperature of aluminium plate

T=95C 70C = 25C Ans. 25

59. The maximum and minimum speeds of a comet that orbits the Sun are 80 and 10 km/s respectively.

The ratio of the aphelion distance of the comet to the radius of the Earths orbit is ___________.

(Assume that Earth moves in a circular orbit of radius 1.5 108km with a speed of 30 km/s)

Solution :

mVara =mVprpm 10 ra =m 80 rp

a

p

r

r =8

1

1

a e

a e

=8 (whereais semimajor axis)

1

1

e

e

=8

e=7

9


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Napehilion of elliptical orbit is given by

2

2 1

L

GMm e=ra ...(1)

In case of circular orbit

2

GMm

r

=

2mV

rGM=V2r ...(2)

L

m=Vara ...(3)

From (1), (2), (3)

2 2

2 1a aV r

V r e=ra

ar

r=

2

2

30 30 71 1

10 9a

Ve

V

=2 Ans. 2

60. If there is a 10% decrease in the atmospheric pressured at a hill compared to the pressure at sea level,then the change in the boiling point of water is _____________C.

(Take latent heat of vaporisation of water is 2270 kJ/kg and the change in the specific volume at the

boiling point to be 1.2 m3/kg.)

Solution :

dP

dT=

2 1

L

T V V

dT= 2 1T V V dP

L

=5373 1.2 0.1 10

2270 1000

=1.97C Ans. 1.97

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IIT Jam 2016 Physics Solutions