0DLQ 3KDVH ,, · Sol. From angular momentum conservation I I I 0 3 C C C 4 m Loss of kinetic energy 2 1 1 2 (1 3 ) 2 2 4 I I 2 1 1 2 2 2 4 I I 3 2 8 I Q.9 A helicopter is rising up

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Q1. Two parallel plate capacitors of capacitance C and 2C are charged upto a potential differecn V and 2Vrespectively. Now these capacitors are connected in parallel to each other such that positive chargedplate of capacitor C is connected to negative charged plate of capacitors 2C. Find amount of change inpotential energy of system.

(1) 2CV (2) 2CV

2(3) 22CV (4) 23CV

Ans. (4)

SOl.

BeforeC,V

– +

–+

2C,V

Charge on C = CVCharge on 2C = (2C) 2V)

After connecting C,V’

–+

–+

2C,V

From charge conservation, 2C(2V)–CV=(C+2C)V’Common potential V’ = V

in finalU U U

2 2 2 21 1 1 1CV 2C 4V CV 2CV2 2 2 2

2U 3CV

2. A bullet of mass 5g moving with a speed of 210 m/s hit a stationary plank and comes to rest. If half ofits kinetic energy is absorbed by bullet itself and remaining half kinetic energy by plank, then findincrease in the temperature of bullet in oC : (Given specific heat of bullet is 6125 J/goC)(1) 1 (2) 1.2 (3) 1.6 (4) 1.8

Ans. (4)Sol. As per given condition

2bullet

1 1 mv (ms T)2 2

3 2 31 1 5 10 (210) (5 10 )(6125)( T)2 2

oT 1.8 C



Q.3 A shell of relative density 279 , is just submerged in water. If its innner and outer radius is r and R

respectively, then rR will be :

(1) 1/31

3

(2) 1/32

3

(3) 1/33

4

(4) 1/35

9

Ans. (2)Sol. In equillibrium

Bmg F

3 3 30

4 4( )3 3 wR r g R g

3

02719 w

rR

3

3

9127

rR

3

3

113

rR

3

3

23

rR

1/323

rR

Q.4 Acceleration due to gravity at height 2Rh is equal to acceleration due to gravity at depth d from the

surface of earth then find d in terms of R. when R is radius of earth.

(1) 43

R (2) 49

R (3) 59

R (4) 3R

Ans. (3)Sol. Given that

n dg g

2 3 ( )( )

GM GM R dR h R

2 3 ( )( / 2)

GM GM R dR R R

2 2

4 19GM GM dR R R

4 19

dR



4 519 9

dR

59

d R

Q.5 Voltage range of Galvanometer of resistance R is 0 to 1V. When it’s range increases up to 2V, for thisthe additional resistance required in series will be :(1) R (2) 2R (3) 3R (4) 4R

Ans. (1)

Soll. gg

V 1iR R

Let the required resistance be r( ) 2gi R r

2R rR

r RQ.6 A uniformly charged sphere of charge Q and radius R is placed at some height from ground surface and

sphere is fixed. Now a charged particle of mass m and charge q is released from rest just below to thesphere. What will be speed of particle after travelling y-distance.

(1) 2gy (2) 2

( )kQq ym R R y

(3) 22

( )kQq ygym R R y

(4) ( )

kQq ygym R R y

Ans. (3)Sol. By using total energy conservation

( ) ( ) 0electro gravitationKE PE PE

21 ( ) 02

Qq Qqmv k k mgyR y R

21 1 12

mv mgy kQqR R y

22( )

kQq yV gym R R y



Q.7 In a photoelectric effect experiment potential difference between plates increases keeping incident lighton cathode plate remains unchanged which of the following is correct about saturation current :(1) Increases (2) Decreases(3) Remain same (4) First increases then decreases

Ans . (3)Sol. Saturation current depends only on intensity of incident light.

Q.8 A disc of momentum of inertia I rotating about its own axis with angular speed . It is placed onanother disc of moment of inertia 3I which is at rest. Both disc have common axis of rotation.What will be the loss of kinetic energy when both discs attain common angular velocity.

(1) 2

8I

(2) 2

4I

(3) 23

8I

(4) 25

8I

Ans. (3)Sol. From angular momentum conservation

0 3C CI I I

4Cm

Loss of kinetic energy2

21 1 (1 3 )2 2 4

I I

221 1

2 2 4I I

238

I

Q.9 A helicopter is rising up from ground with an acceleration of g m/s2 starting from rest. after rising aheight h, it attain a velocity of v m/s. At this instant a particle is now released from helicopter .Take t=0at releasing time calculate the time t when particle reaches to the ground.

(1) 2hg (2)

22 hg (3) 21 2

hg (4)

24 hg

Ans. (3)

Sol.



For upward motion of helicopter2 2 2v u as 2 0 2v gh

2v gh

Now particle will start moving under gravity..

212

s ut at

2122

h ght gt

21 2 02

gt ght h

than

2 2 42

22

ggh gh ht g

2 (1 2)ghtg

2 (1 2)htg

10. Which of the following graph represents relation between the image position (v) and object position (u)from the concave lens.

(1) (2) (3) (4)

Ans. (1)

Sol. By using relation 1 1 1v u f

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0DLQ 3KDVH ,, · Sol. From angular momentum conservation I I I 0 3 C C C 4 m Loss of kinetic energy 2 1 1 2 (1 3 ) 2 2 4 I I 2 1 1 2 2 2 4 I I 3 2 8 I Q.9 A helicopter is rising up