When a ball of mass \(5\ \text{kg }\)hits a bat with a velocity \(3\ \text{m/s}\), in the positive direction, and it moves back with a velocity \(4\ \text{m/s}\). The impulse in SI units is:

1. \(5 \)

2. \(15\)

3. \(25\)

4. \(35\)

A particle of mass \(m\) has momentum \(p\). Its kinetic energy will be:
1. \(mp\)
2.  \(p^2 𝑚\)
3.  ​​​​​​​\(\dfrac{𝑝^ 2}m\)
4.  \(\dfrac{𝑝^ 2}{2m}\)

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

1. \(15\left(5\hat{i}+6\hat{j}+5\hat{k}\right)\)
2.  \(15\left(5\hat{i}+6\hat{j}-5\hat{k}\right)\)
3. \(150\left(5\hat{i}-6\hat{j}+5\hat{k}\right)\)
4. \(150\left(5\hat{i}+6\hat{j}+5\hat{k}\right)\)

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. \(\dfrac{F^2t^2}{m}\)

2. \(\dfrac{F^2t^2}{2m}\)

3. \(\dfrac{F^2t^2}{3m}\)

4. \(\dfrac{Ft}{2m}\)

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 \(\vec{v}_i=5\hat{i}-3\hat{j}+7\hat{k}\ \text{m/s}\)  to \(\vec{v}_f=2\hat{i}+3\hat{j}+\hat{k}\ \text{m/s}\) is: 
1. \(2.7\ \text{N-s}\)
2. \(1.8\ \text{N-s}\)
3. \(0.9\ \text{N-s}\)
4. \(3.6\ \text{N-s}\)

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

1.  \(75\ \text{N}\)
2.  \(150\ \text{N}\)
3.  \(300\ \text{N}\) 
4.  \(600\ \text{N}\) 

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

A small block of mass \((m=1\ \text{kg})\) is placed on the smooth inclined surface of a triangular wedge of mass \((M'=4\ \text{kg})\). The wedge rests on a smooth horizontal surface. A horizontal string connects the small block to a hanging block of mass \(M\) through a fixed, frictionless pulley, as shown in the figure.
If the inclination of the wedge is \(\theta=37^\circ\), find the value of \(M\) for which the small block does not slip relative to the wedge. Assume the string is light and inextensible.

           
1. \(12\) kg
2. \(15\) kg
3. \(10\) kg
4. \(4\) kg