A string of negligible mass going over a clamped pulley of mass $m$ supports a block of mass $M$ as shown in the figure. The force on the pulley by the clamp is given by:
 
1. $\sqrt{2} M g$
2. $\sqrt{2} m g$
3. $g\sqrt{\left( M + m \right)^{2} + m^{2}}$
4. $g\sqrt{\left(M + m \right)^{2} + M^{2}}$

A pulley fixed to the ceilling carries a string with blocks of mass m and 3 m attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with what acceleration 

1. 0

2. g/4

3. g/2

4. –g/2

A block $B$ is placed on top of block $A$. The mass of block $B$ is less than the mass of block $A$. Friction exists between the blocks, whereas the ground on which block $A$ is placed is assumed to be smooth. A horizontal force $F$, increasing linearly with time begins to act on $B$. The acceleration $a_A$ and $a_B$ of blocks $A$ and $B$ respectively are plotted against $t$. The correctly plotted graph is:

1.		2.
3.		4.

The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in time interval from zero to 8 second will be 

1. – 2 N-s

2. + 4 N-s

3. 6 N-s

4. Zero

A body of 2 kg has an initial speed 5ms^–1. A force acts on it for some time in the direction of motion. The force time graph is shown in figure. The final speed of the body.

1. 9.25 ms^–1

2. 5 ms^–1

3. 14.25 ms^–1

4. 4.25 ms^–1

A particle of mass m, initially at rest, is acted upon by a variable force F for a brief interval of time T. It begins to move with a velocity u after the force stops acting. F is shown in the graph as a function of time. The curve is an ellipse.

1. $u=\frac{\pi F_0^2}{2m}$

2. $u=\frac{\pi T^2}{8m}$

3. $u=\frac{\pi F_{0}T}{4m}$

4. $u=\frac{F_{0}T}{2m}$

A body of mass 3kg is acted upon by a force which varies as shown in the graph below. The momentum acquired is given by

1. Zero

2. 5 N-s

3. 30 N-s

4. 50 N-s

The variation of momentum with the time of one of the bodies in a two-body collision is shown in fig. The instantaneous force is the maximum corresponding to the point:
             
1. $P$
2. $Q$
3. $R$
4. $S$

Figures I, II, III and IV depict variation of force with time.

(I)
(II)
(III)
(IV)

The impulse is highest in the case of situations depicted. Figure

1. I and II

2. III and I

3. III and IV

4. IV only

The masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has acceleration 12 m/sec². What is the acceleration of 20 kg mass?

1. 12 m/sec²

2. 4 m/sec²

3. 10 m/sec²

4. Zero