A cricketer catches a ball of mass \(150~\mathrm{gm}\) in \(0.1\) \(\mathrm{s}\) moving with a speed of \(20~\mathrm{ms^{-1}}\). Then he experiences a force of:
1. \(300~\mathrm{N}\)
2. \(30~\mathrm{N}\)
3. \(3~\mathrm{N}\)
4. \(0.3~\mathrm{N}\)
 

A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of \(12\) m/s. If the mass of the ball is \(0.15\) kg, then the impulse imparted to the ball is:
(Assume linear motion of the ball.)
1. \(0.15\) N-s
2. \(3.6\) N-s
3. \(36\) N-s
4. \(0.36\) N-s

Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get reflected without any change in speed, as shown in the figure. The ratio of the magnitudes of impulses imparted to the balls by the wall is:

1. \(2:3\)
2. \(\sqrt{3}:2\)
3. \(2:\sqrt{3}\)
4. \(1:1\)

See the figure given below. A mass of \(6\) kg is suspended by a rope of length \(2\) m from the ceiling. A force of \(50\) N is applied at the mid-point \(P\) of the rope in the horizontal direction, as shown. What angle does the rope make with the vertical in equilibrium? (Take \(g=10\) ${\mathrm{ms}}^{-2}$). Neglect the mass of the rope.

Determine the maximum acceleration of the train in which a box lying on its floor will remain stationary, given that the coefficient of static friction between the box and the train’s floor is \(0.15.\)
1. \(0\)
2. \(0.5~\mathrm{m/s^2}\)
3. \(2.5~\mathrm{m/s^2}\)
4. \(1.5~\mathrm{m/s^2}\)

See the figure given below, a mass of \(4\) kg rests on a horizontal plane. The plane is gradually inclined until at an angle \(\theta=15^\circ\) with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?

In the figure given below, a wooden block of mass \(2\) kg rests on a soft horizontal floor. When an iron cylinder of mass \(25\) kg is placed on top of the block, the floor yields steadily and the block and the cylinder together go down with an acceleration of \(0.1~\mathrm{m/s^2}\). What is the force of the block on the floor after the floor yields? (Take \(g=10~\mathrm{m/s^2}\)${\mathrm{}}^{}$.)
     
1. \(270\) N upward
2. \(267.3\) N downward
3. \(20\) N downward
4. \(267.3\) N upward

Calculate the acceleration of the block and trolly system shown in the figure. The coefficient of kinetic friction between the trolly and the surface is \(0.05\).
( \(g=10 \mathrm{~m} / \mathrm{s}^2\), mass of the string is negligible and no other friction exists ). 

           
1. \( 1.25 \mathrm{~m} / \mathrm{s}^2 \)
2. \( 1.50 \mathrm{~m} / \mathrm{s}^2 \)
3. \( 1.66 \mathrm{~m} / \mathrm{s}^2 \)
4. \( 1.00 \mathrm{~m} / \mathrm{s}^2\)

A body of weight \(\mathrm{w}_{1}\) is suspended from the ceiling of a room through a chain of weight \(\mathrm{w}_{2}.\)The ceiling pulls the chain by a force:
1. \(\mathrm{w}_{1}\)
2. \(\mathrm{w}_{2}\)
3. \(\mathrm{w}_{1}+\mathrm{w}_{2}\)
4. \(\frac{\text w_{1}+\text w_{2}}{2}\)

When a horse pulls a cart, the force that helps the horse to move forward is the force exerted by: