1. Two blocks of masses 1m (= 1 kg) and 2m (= 2kg) connected by a weightless spring of stiffness

k (= 0.2 N/m) rest on a smooth horizontal plane as shown in figure. Block 2 is shifted a small

distance x (= 0.1m) to the left and then released. Find the velocity (in cm/s) of centre of mass of the system after block 1 breaks off the wall.

km2m1

1 2

wall

2. A ball is thrown upwards from the ground with an initial speed of u. The ball is at a height of 80

m at two times, the time interval being 6s. If u = n × 10 (in m/s). Then n is equal to (Take g = 10

m/s2)

3. A block slides down a smooth inclined plane to the ground when released at the top, in time t

seconds. Another block is dropped vertically from the same point, in the absence of the inclined plane and reaches the ground in t/2 second. The angle (in degree) of inclination of the plane with

the vertical is 60°/n where n is.

4. A uniform chain of mass M (= 1 kg ) and length L ( =10 cm) lies on a frictionless table with

length 0l 6cm hanging over the edge. The chain begins to slide down. The speed (in m/s) with

which the chain slides away from the edge is 2

n where n is (Take g = 1000 cm/s

2)

A U shaped tube of mass 2 m is placed on a smooth horizontal

surface. Two identical spherical balls each of mass m and of diameter slightly less than the inner diameter of tube enters

into the tube with a velocity u as shown in the figure. (Assume

no loss of energy anywhere and all collisions to be elastic)

Bm

Am

5. Speed of each spherical ball, just before their collision

(a) u

3 (b)

2u

3

(c) 3u

2 (d)

u

2

6. At the time of collision, angle between direction of motion of spherical ball a and B is, as observed in the ground frame,

(a) 12tan 2 (b) 1 1

2tan2

(c) 1tan 2 (d)

7. A particle of mass m is moving in a potential well, for which the potential energy is given

by U(x) = Uo(1 - cos ax) where Uo and a are constants. Then (for the small oscillations)

(a) the time period of small oscillations is T = o

m2

aU

(b) the speed of the particle is maximum at x = 0

(c) the amplitude of oscillations is 2a

(d) the time period of small oscillations T = 2

o

m2

a U

8. A disc of mass M and radius R moves in the x-y

plane as shown in the figure. The angular

momentum of the disc at the instant shown is

(a) 5

2mR

2 about O (b)

7

2mR

2about O

(c) 1

2mR

2about A (d) 4mR

2about A

4R

3R

v = R

x

y

A

B O

9. Two light vertical springs with equal natural lengths and spring constants k1 and k2 are separated by a distance l. Their upper ends are

fixed to the ceiling and their lower ends to the ends A and B of a light

horizontal rod AB. A vertical downwards force F is applied at point C on the rod. AB will remain horizontal in equilibrium if the distance

AC is

A B F

l k1 K2

C

(a) l

2 (b) 1

2 1

lk

k k

(c) 2

1

lk

k (d) 2

1 2

lk

k k

10. A cylinder of height h diameter h/2 and mass M and with a homogenous

mass distribution is placed on a horizontal table. One end of a string

running over a pulley is fastened to the top of the cylinder, a body of

mass m is hung from the other end and the system is released. Friction is negligible everywhere. At what minimum ratio M/m will the cylinder

tilt?

h/2

M

m

(a) 1 (b) 2 (c) 3 (d) 4