Physics Paper - i

CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA # 1

PHYSICS PAPER - I (ADVANCED)

1. The magnetic field inside a solid conducting long wire at distance r from its axis is given as 30B B r

where B0 is constant. Which of the following relations correctly represents current enclosed in the loopof radius r shown in the figure :

r

(a) 5

0

0

2 B r5 (b)

40

0

B r2 (c)

20

0

2 B r (d)

40

0

2 B r

2. A proton is bombarded on a stationary lithium nucleus. As a result of the collision two -particles areproduced. If the direction of motion of the -particles with the initial direction of motion of the proton

makes an angle

1 1cos

4, the kinetic energy of the striking proton is : [Given, binding energies per

nucleon of Li7 and He4 are 5.60 MeV and 7.06 MeV respectively. Assume mass of proton = mass ofneutron](a) 5.14 MeV (b) 17.28 MeV (c) 34.56 MeV (d) 68.32 MeV

SPACE FOR ROUGH WORK

PART I : PHYSICS

SECTION I : SINGLE CHOICE QUESTIONS

This section contains 10 multiple choice questions. Each question has four choices(A), (B), (C) and (D) out of which ONLY ONE is correct.



3. For an ideal gas V-T graph is as shown in the figure. If at A and B pressures of gas are PA and PBrespectively then :

V

A

B

T(K)

(a) BA PP (b) BA PP (c) BA PP (d) BA PP

4. In the following diagrams, P, Q, R are three air molecules. The arrows indicate their relative amplitudeand direction of vibration. Determine which of the diagrams may correctly indicate the vibration of the airmolecules of the open pipe emitting its fundamental note.

(a) P Q R

o o o (b) P Q Ro o o

(c) PQ

Ro o o (d) P

QR

o o o

5. A rain drop of radius 1.5 mm, experiences a drag force, 5F (2 10 v)N , while falling through airfrom a height of 2 km with a velocity v. The terminal velocity of the rain drop will be nearly :(a) 200 m/s (b) 80 m/s (c) 7 m/s (d) 3 m/s



PHYSICS PAPER - I (ADVANCED)6. Two coherent point sources S1 and S2 vibrating in phase emit light of wavelength . The

separation between them is 2 . The light is collected on a screen placed at a distance D >> as shown in figure. The minimum distance x so that intensity at P is equal to intensity at O is :

(a) D (b) D/3 (c) 3 D (d) D/2

7. An aircraft flies at 400 km/hr in still air. A wind of 2200 km/hr is blowing towards northwith respect to earth. The aircraft has to travel from point A to a point B north east of A. Theaircraft must be steered at angle ............. from north towards east :(a) 30º (b) 45º (c) 75º (d) 15º.

8. In the circuit shown the equivalent resistance between A and B is :

2R 2R 2R

8AB R R R

(a) zero (b) R (c) (1 3)R (d) 3R




9. A progressive sinusoidal wave of amplitude 2.5 cm, wavelength 30 cm and frequency 30 Hzis superposed on a similar wave travelling in the opposite direction to form standing wavepattern. The magnitude of the maximum velocity of particle at x / 4 , (where x = 0 is anode) is:(a) 900 cm/sec (b) 942 cm/sec (c) 10 cm/sec (d) 0

10. An infinite, uniformly charged sheet with surface charge density passes through a sphericalGaussian surface of radius R at a distance x from its center, as shown in the figure. Theelectric flux through the Gaussian surface is :

xR

(a) 2

0

R (b)

2

0

2 R (c)

2

0

(R x) (d)

2 2

0

(R x )




SECTION II: (MULTIPLE CHOICE QUESTIONS)

This section contains 5 multiple choice questions. Each question has four choices(A), (B), (C) or (D) out of which ONE or MORE is/are correct.

11. The magnitudes of the electric field at distance r1 and r2 from the centre of a uniformlycharged sphere of radius R, are E1 and E2 respectively, then :

(a) 1 11 2

2 2

E rif r R and r R

E r (b)

21 1

1 222 2

E rif r R and r R

E r

(c) 2

1 21 22

2 1

E rif r R and r R

E r (d)

21 1

1 222 2

E rif r R and r R

E r

12. Two charge particles each of charge q and masses m1 and m2 moving with equal kineticenergies when enter into a uniform magnetic field perpendicular to it, m1 forms circularpath of bigger radius, then :(a) m1 > m2

(b) ratio of magnitude of their linear momenta i.e., 1

2

P1

P

(c) ratio of de-Broglie wavelengths associated with charge particles i.e., 1

2

1

(d) 1

2

m1

m




13. Starting with same initial conditions, an ideal gas expands from volume V1 and V2 under theprocess PVn = constant where 0 n 1.4 . Workdone by gas :(a) will be minimum for n = 1 (b) will be maximum for n = 0(c) will be minimum for n = 1.4 (d) will be maximum for n = 1.4

14. The continuous X - ray spectrum for the three potential differences between target andcathode, V1, V2 and V3 is shown. Temperatures of filament in these cases are T1, T2 and T3respectively, then :

V3

V2

V1

Inte

nsity

(I)

T 3T2

T1

(a) 321 VVV (b) 321 TTT (c) 321 VVV (d) 321 TTT

15. If a light ray passes through prism as shown in the figure then :

r1 r2

µ= 2

A

(a) A = 90º (b) deviation produced is minimum(c) r1 = r2 = 45º (d) angle of incidence = angle of emergence



PHYSICS PAPER - I (ADVANCED)SECTION III: INTEGER VALUE CORRECT TYPE

This section contains 5 questions. The answer to each question is a single digitinteger, ranging from 0 to 9 (both inclusive)

16. A satellite in force-free space collects stationary interplanetary dust at a rate

vdt

dM

where M is instantaneous mass of satellite and is positive constant. Find

velocity (in m/s) of satellite at time t = 4 sec if kM , where 15

k ,[At t = 0, velocity of

satallite is 5 m/s]

17. A narrow parallel beam strikes the glass sphere of refractive index 1.5 and radius 15 cmalong a diameter. The distance from centre of sphere at which the beam will converge is4.5x0 cm. Find x0.

18. When a metal slab of thickness less than separation between plates of parallel plate capacitoris kept parallel to plates as shown the capacitance increase by 20% .When metal slab isreplaced by a dielectric slab, capacitance increases by 10 % of initial value(air capacitor).The dielectric constant of dielectric slab is 1.1k0. Find k0




19. A long object of mass m and cross-section area a is attached with spring of spring constant k.When spring is relaxed, the object just touches non viscous liquid (density ) surface as shown.The area of container is A. If the block is released then the maximum displacement, the objecttravels downward is 0.009 x0 m. Find x0.[ m = 10kg, g = 10m/s2, a = 2m2,A =10m2, 3200kg / m , k = 500N/m]

20. AB is 1 meter long uniform wire of 10 resistance. Other data are shown in the followingdiagram. The potential gradient along AB is 0.001 V0 Volt/cm. Find V0.

A

15

1.2

0.3

2V

1.5V

B

O

G


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Physics Paper - i