1. Consider the situation shown in the figure.

50 m/s 50 m/s

3 m m

A B60 m

Two particles are at same horizontal levels, moving with 5 m/s in opposite direction. During collisionthe particles stick to each other. At what distance from A the combined particle will land. 210 /g m s=(initial height of particles is equal to 20 m)(a) 30 m (b) 35 m(c) 40 m (d) 50 m

2. A 10 g bullet moving 1000 m/s strikes and passes through a 2.0 kg block initially at rest, as shown.The bullet emerges from the block with a speed of 400 m/s. To what maximum height will the blockrise above its initial position?

(a) 66 cm(b) 56 cm

v(c) 46 cm(d) 37 cm

3. Three small bodies with the mass ratio 3:4:5 (the mass of the lightest body is m) are kept at threedifferent points on the inner surface of a smooth hemispherical cup of radius r. The cup is fixed at itslowest point on a horizontal surface. At a certain instant, the bodies are released.

What is the maximum amount of heat that can be liberated in such a system. Assume that collisionsare perfectly inelastic.(a) 4mgr (b) 3mgr(c) 2mgr (d) mgr

4. Choose the wrong statement : In head-on elastic collision of two bodies of equal masses:(a) the velocities are interchanged(b) the speeds are interchanged(c) the momentum are interchanged(d) the faster body slows down and the slower body speeds up.

5. Two particles having position vectors 1 (3 5 )r i j= +! !! meter and 2 ( 5 3 )r i j=

! !! meter are movingwith velocities 1 (4 3 )v i j= +

! !! m/s and 2 ( 7 )v ai j= +! !! m/s. If they collide after 2 second, the value of

a is:(a) 2 (b) 4(c) 6 (d) 8.

6. Consider the situation shown in the figure. A small ball of mass m hits a rough horizontal surface(fixed)with speed u at an angle with the vertical. What is the horizontal component of the balls velocityimmediately after the impact?

u

m

,e

(a) sinu (b) cose u (c) [sin cos (1 )]u e + (d) [sin sin ]e

7. A ball of mass m is released from a height h above a fixed horizontal surface. If e be the coefficientof restitution, the total momentum transferred to the surface when it finally comes to rest after a longtime is

h

m

e

(a)121

em ghe

+

(b)121

em ghe

+

(c)11

em ghe

+

(d)11

em ghe

+

8. A uniform rod of mass m and length l is placed in x-y plane. At each point of the rod a force parallelto the x-axis is applied, as shown in figure. At position y, force per unit length of rod, ,xf is given byky. What is the net torque on the rod about the z-axis at the moment shown in figure?

O

f =kyx

y

m,l

y

x

(a)2

3kl

(b)2

2kl

(c) 323

kl (d)3

3kl

9. A uniform rod AB of length l is moving in a horizontal plane. At a certain moment velocities of endsA and B are as shown in the figure. At the same moment what is the speed of centre C, of the rod?

A

B

C

45

45v

v

(a) / 2v (b) / 2v(c) 2v (d) 2v

10. Two circus clowns (each having a mass of 50 kg) swing on two flying trapezes (negligible mass,length 25 m) shown in the figure. At the peak of the swing, one grabs the other, and the two swing backto one platform. The time for the forward and return motion is

(a) 10 s (b) 50 s(c) 15 s (d) 20 s

11. The diagrams below show forces applied to a wheel that weighs 20 N. The symbol W stands for theweight. In which diagram is the wheel in equilibrium?

20 N

10 N

10 N

W(A)

20 N

10 N

10 N

W(B)

5 N

W

5 N

(C)

10 N

W10 N

(D)

(a) A (b) B(c) C (d) D

12. The system of the wedge and the block connected by a massless spring as shown in the figure isreleased from rest with the spring in its natural length. Friction is absent everywhere. What is themaximum elongation in the spring ?

M

k

M37

(a)mgk (b)

2 mgk

(c)56

mgk (d)

65

mgk

13. The acceleration a of the plank P required to keep the centre C of a cylinder in a fixed positionduring the motion is :

(No slipping takes place between cylinder and plank)

(a) sin2g

(b) 2 sing

a

PC

(c) sing

(d) 2 sing

14. A bullet of mass m moving with velocity u just grazes the top of a solid cylinder of mass M andradius R resting on a rough horizontal surface as shown in the figure. Assume the cylinder rollswithout slipping. Find the velocity of centre of mass of the sphere.

(a)4

(8 3 )mRu

m M+

(b)4

(4 3 )mu

m M+ C

friction

um

(c)m u

m M

+ (d) ( )

mum M R+

15. The friction coefficient between the horizontal surface and each of the blocks shown in figure is0.20. The collision between the blocks is perfectly elastic. Find the separation between the twoblocks when they come to rest ( 210 /g m s= )

2 kg 4 kg

1.0 m/s

16 cm(a) 2cm (b) 3cm(c) 4cm (d) 5cm

16. A particle of mass 1m collides elastically with a stationary particle of mass 2 1 2( ).m m m> Find themaximum angle through which the striking particle may deviate as a result of the collision.

(a) 1 12

sin mm

= (b)1 2

1

sin mm

= (c) 90 = (d) 1 2

1

tan mm

= 17. A hoop, a solid cylinder, and a solid sphere all have the same mass m and the same radius R. Each is

mounted to oscillate about an axis a distance 0.5 R from the center. The axis is perpendicular to thecircular plane of the hoop and the cylinder and to an equatorial plane of the sphere as shown below.Which is the correct ranking in order of increasing angular frequency ?

(a) hoop, cylinder, sphere (b) cylinder, sphere ,hoop(c) sphere, cylinder, hoop (d) hoop, sphere, cylinder(e) sphere, hoop, cylinder

18. A water tank resting on the floor has two small holes vertically one above the other. The holes are

1h cm and 2h cm above the floor. How high does water stand in the tank if the jets from the holes hitthe floor at the same point.(a) 1 2( )h h+ (b) 2 1( )h h

(c)2 2

1 2

2h h + (d)

2 22 1

2h h

19. Two separate air bubbles (radii 0.002 m and 0.004 m) formed of the same liquid (surface tension0.07 N/m) come together to form a double bubble. Find the radius of curvature of the internal filmsurface common to both the bubbles.

R2R1

(a) 0.002 m (b) 0.004 m(c) 0.003 m (d) 0.005 m

20. Two equal drops of water are falling through air with a steady velocity v. If the drops coalesced,what will be the ratio of new steady velocity to the older value. The value of coefficient of viscosityof air is 2 SI unit.(a) 2/32 (b) 1/32(c) 2/32 2 (d) 2

21. Figure shows a L-shaped tube in which a liquid of density is filled. Find with what acceleration thetube is accelerated toward right so that no liquid will fall out of the tube.

(a)hgl (b)

2ghl

l

ah

(c)3hg

l (d)4 hg

l

22. A sphere of radius R, made from material of specific gravity SG, is submerged in a tank of water. Thesphere is placed over a hole, of radius a, in the tank bottom. For the dimensions given, determine theminimum SG required for the sphere to remain in the position shown.

R mm = 20

a mm = 2

H = 0.8 m

(a) 0.70SG > (b) 0.65SG >(c) 0.60SG > (d) 0.75SG >

23. A particle is fired vertically upward with a speed of 9.8 / .km s Find the maximum height attained by

the particle. Radius of earth = 64000 km 29.8 / .g m s=(a) 20000 km (b) 18000 km(c) 20900 km (d) 18900 km

24. A double star is a system of two stars moving around the centre of inertia of the system due togravitation. Find the distance between the components of double stars. If its total Mass is M andperiod of revolution is T.

(a)2

324

G MT

(b)2

3

4G MT

(c)2

32

G MT

(d) None

25. Gagrine, the russian astronaut, decided to move freely in the space, so he tied his body with a cordof length l, connected it to his spaceship, whose mass is much larger than the mass of astronaut.Assume that space-ship is orbiting near earth surface and ship and astronaut fall in astraight line from the earths centre.The tension in the cord will be:( given 6400R km= 64l m= and Mass of astronaut = 100 kg.)

(a) 22 10 N (b) 23 10 N

(c) 24 10 N (d) 25 10 N

26. Suppose, force of gravitation doesnt follow inverse square law rather the force is now inversely

proportional to the cube of distance between particles. Then what will be the corresponding changein Keplers law.

( T = time - period ; a = length of the semi major axis)(a) 2 3T a (b) 2 4T a

(c) T is independent of a (d)1

Ta

27. If the time period of a satellite TS is different from that of earths rotation TE and the satellite ismoving in the direction of earths rotation, the time interval between two successive appearances ofthe satellite overhead, T, is given by

(a)1 1 1

S ET T T= (b) T = TS ~ TE

(c)1 1 1= +

S ET T T(d) T = TS + TE

28. The optimal way of transferring a space vehicle from an innercircular orbit to an outer coplanar circular orbit is to fire itsengines as it passes through A to increase its speed and place itin an elliptic transfer orbit. Another increase in speed as itpasses through B will place it in the desired circular orbit. Fora vehicle in a circular orbit about the earth at an altitude

1 320h = km, which is to be transferred to a circular orbit at analtitude 2 800h = km. What is the required increase in speedat A? (Radius of the earth is 6370 km)(a) 147 /m s (b) 157 /m s

h1 h2

Plane

Earth

RA B

(c) 167 /m s (d) 117 /m s

29. The equation of FM signals by Radio Mirchi and Red FM are of the form of SHM, and given below:

Red FM (93.5) 1 1 1sinx A w t= ; frequency = 93.5 2MH .

Radio Mirchi (98.3) 2 2 2sinx A w t= ; frequency = 98.3 2MH .

Due do some fault in tuner, the radio set start catching both singals. So the signals superimposed andthere is a noise caused by oscillation of amplitude of resulting signal. What will be the frequency ofoscillation of amplitude of resulting signal.

(a) 64.8 10 Hz (b) 6191.8 10 Hz

(c) ( )6 21

1.05 10 wHz w (d) zero.

30. The escape velocity for a planet is 20 km/s. What is the potential energy of a particle of mass 1 mgon the surface of this planet.(a) 200 J (b) 175 J(c) 165 J (d) 195 J

[ CIRCLE 3]

1. Choose the correct statementThe use of 12 C scale has an advantage over the older scale of atomic mass based on 16 O isotope.because(a) The atomic masses on 12 C become whole numbers.(b) 12 C is more abundant in the earths curst than 16 .O(c) The difference between the physical and chemical atomic masses got narrowed down significantly.(d) 12 C is situated midway between metals and non metals in the periodic table.

Ans (c)2. The ionization energy of a hydrogen atom is 13.6 ev. The energy of the third lowest electronic level

in doubly ionized lithium (z = 3) is(a) 28.7 ev (b) 54.4 ev(c) 122.4 ev (d) 13.6 ev.

Ans (c)

3. 1.0 g of a mixture of 3NaHCO and 2 3Na CO is heared to 150C. The volume of the 2CO producedat STP is 112.0 ml. Calculate the percentage of 2 3Na CO in the mixture ( 23, 12, 16)Na C O= = =(a) 20 (b) 40(c) 84 (d) 16

Ans (d)4. The number of moles of 22 7CO O

needed to oxidize 0.136 equivalent of 2 5N H+ through the reaction

2 32 5 2 7 2 2N H Cr O N Cr H O

+ ++ + +

(a) 0.236 (b) 0.087(c) 0.136 (d) 0.488

Ans (c)5. An impure sample of silver weighing 2.50 g is dissolved in 3HNO and the silver is precipitated to

yield 2.50 .g AgCl What is the percentage by weight of silver in the original sample( 108, 35.5).Ag Cl= =(a) 75.26 (b) 100.0(c) 50.26 (d) 88.45

Ans (a)6. According to Einsteins photoelectric equation, the graph between the kinetic energy of photoelectrons

ejected and the frequency of incident radiation is

(a)

frequency

KE

(b)

frequency

KE

(c)

frequency

KE

(d)

frequency

KE

7. Which of the following statements is incorrect ?(a) The second ionization energy of sulpher is greater than that of chlorine(b) The third ionization energy of phosphorus is greater than that of aluminium(c) The first ionization energy of aluminium is approximately the same as that of gallium.(d) The second ionization energy of boron us greater than that of carbon.

Ans (a)

8. Which of the following is arranged in order of increasing boiling point ?(a) 2 4 2 2H O CCl CS CO< < < (b) 2 2 4 2CO CS CCl H O