A particle of mass m at rest is acted upon by a constant force F for a time t. Its kinetic energy after an interval t is 

1.  $\frac{{\mathrm{F}}^2{\mathrm{t}}^2}{\mathrm{m}}$

2.  $\frac{{\mathrm{F}}^2{\mathrm{t}}^2}{2\mathrm{m}}$

3.  $\frac{{\mathrm{F}}^2{\mathrm{t}}^2}{3\mathrm{m}}$

4.  $\frac{\mathrm{Ft}}{2\mathrm{m}}$

For a rocket moving in free space, the fraction of mass to be disposed of Off to attain a speed equal to two times the exhaust speed is given by (given ${\mathrm{e}}^2$ = 7.4)

1.  0.40

2.  0.37

3.  0.50

4.  0.86

The magnitude of the impulse developed by a mass of 0.2 kg which changes its velocity from $5\hat{\mathrm{i}} - 3\hat{\mathrm{j}} + 7\hat{\mathrm{k}} \mathrm{m}/\mathrm{s} \mathrm{to} 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + \hat{\mathrm{k}} \mathrm{m}/\mathrm{s}$ is

1.  2.7 N-s

2.  1.8 N-s

3.  0.9 N-s

4.  3.6 N-s

A particle of mass m has momentum p. it's kinetic energy will be 

1.  mp

2.  $p^{2}m$

3.  $\frac{p^2}{m}$

4.  $\frac{p^2}{2m}$

When a ball of mass = 5kg hits a bat with a velocity = 3 m/s, in positive direction and it moves back with a velocity = 4 m/s, find the impulse in SI units

1. 5 

2. 15

3. 25

4. 35

A soldier is firing 20 bullets per second from his gun having a muzzle speed of 150 m/s. The mass of each bullet is 50 g. If they strike the wall and rebound with the same speed, then the force on the wall is

1.  75 N

2.  150 N

3.  300 N

4.  600 N

A simple pendulum hangs from the roof of a train moving on horizontal rails. If the string is inclined towards the front of the train, then train is-

1. Moving with constant velocity

2. In accelerated motion

3. In retarded motion

4. At rest

The value of $M$ of the hanging block is in the figure, which will prevent the smaller block ($m$$=$$1$ kg) from slipping over the triangular block. All the surfaces are smooth and string and pulley are ideal. (Given: $M'$$=4$ kg and $\theta$ $=37^\circ$)

           
1. $12$ kg
2. $15$ kg
3. $10$ kg
4. $4$ kg