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 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.  $\frac{\mathrm{Ft}}{2\mathrm{m}}$

A particle of mass 15 kg has an initial velocity ${\mathrm{v}}_{\mathrm{i}} = \hat{\mathrm{i}} - 2\hat{\mathrm{j}}$ m/s. It collides with another body and the impact time is 0.1 s, resulting in a velocity ${\mathrm{v}}_{\mathrm{f}} = 6\hat{\mathrm{i}} + 4\hat{\mathrm{j}} + 5\hat{\mathrm{k}}$ m/s after impact. The average force of impact on the particle is

1.  $15\left|5\hat{\mathrm{i}} + 6\hat{\mathrm{j}} + 5\hat{\mathrm{k}}\right|$

2.  $15\left|5\hat{\mathrm{i}} + 6\hat{\mathrm{j}} - 5\hat{\mathrm{k}}\right|$

3.  $150\left|5\hat{\mathrm{i}} - 6\hat{\mathrm{j}} + 5\hat{\mathrm{k}}\right|$

4.  $150\left|5\hat{\mathrm{i}} + 6\hat{\mathrm{j}} + 5\hat{\mathrm{k}}\right|$

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