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

A lighter body and a heavier body are both moving with the same momentum and are subjected to the same retarding force. Their stopping distances are \(s_1\) and \(s_2\) respectively. Then the correct relation between ${}_{}$ \(s_1\) and \(s_2\)  is:

1. \(s_1 >s_2\)

2. \(s_1<s_2\)

3. \(s_1=s_2\)

4. None of these

A simple pendulum (bob of mass \(m\)) oscillates in a vertical plane. Let \(\theta\) be the angular displacement from the vertical. The tension in the string is equal to \(mg \cos\theta\) under which condition?
1. Always
2. Never
3. At the extreme position
4. At the mean position

The graph for stopping time \((t)\) versus mass \((m)\) is shown in the figure. Then which one of the pairs is given?

1. Momentum, force

2. K.E., force

3. Velocity, force

4. None of these

A metal ring of mass \(m\) and radius \(R\) is placed on a smooth horizontal table and is set to rotate about its own axis in such a way that each part of the ring moves with a speed \(v\).

The tension in the ring is:

1. \(\dfrac{mv^2}{R}\)
2. \(\dfrac{mv^2}{2R}\)
3. \(\dfrac{mv^2}{2\pi R}\)
4. \(\text{None of these}\)

Tension on the string at point \(P\) is \(T\). The graph for tension \((T)\) versus \(x\) is shown in the figure. Then the string is: