The figure shows the position-time graph of a particle of mass \(4~\text{kg}\). What is the force on the particle for \(t>4~\text{s}\)? 
(Consider one-dimensional motion only).

            

1.	\(0\)	2.	\(40~\text{N}\)
3.	\(20~\text{N}\)	4.	\(10~\text{N}\)

Two billiard balls each of mass 0.05 kg moving in opposite directions with speed 6 m/s collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
1. \(0.4 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\)
2. \(0.3 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\)
3. \(0.6 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\)
4. \(0.7 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}\)

A stone of mass \(0.25\) kg tied to the end of a string is whirled around in a circle of radius \(1.5\) m with a speed of \(40\) rev/min in a horizontal plane. The tension in the string is:
1. \(5.6\) N
2. \(6.6\) N
3. \(3.4\) N
4. \(4.2\) N

The figure shows a man of mass \(65\) kg standing stationary with respect to a horizontal conveyor belt that is accelerating with \(1\) ms^-2. If the coefficient of static friction between the man’s shoes and the belt is \(0.2,\) up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Take \(g=10\) m/s²)

  
 

1.	\(2\) ms-2	2.	\(3\) ms-2
3.	\(1\) ms-2	4.	\(9.8\) ms-2

(${\mathrm{}}_{}$\(T_1\) and \(v_1\) denote the tension and speed at the lowest point.${\mathrm{}}_{}$ \(T_2\) and \(v_2\) denote corresponding values at the highest point.)

A helicopter of mass 1000 kg rises with a vertical acceleration of $15 {\mathrm{ms}}^{-2}$. The crew and the passengers weigh 300 kg. The magnitude and direction of the action of the rotor of the helicopter on the surrounding air are:

$1. 3.25\times {10}^4 \mathrm{N} \left(\mathrm{upwards}\right)$
$2. 3.25\times {10}^4 \mathrm{N} \left(\mathrm{downwards}\right)$
$3. 7.5\times {10}^3 \mathrm{N} \left(\mathrm{upwards}\right)$
$4. 7.5\times {10}^3 \mathrm{N} \left(\mathrm{downwards}\right)$

A stream of water flowing horizontally with a speed of \(15\) ms^–1 pushes out of a tube of cross-sectional area \(10^{-2}\) m² and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound? (Density of water, \(\rho=10^{3}\)  kg-m^–3)

An aircraft executes a horizontal loop at a speed of \(720\) km/h with its wings banked at \(15^{\circ}\). What is the radius of the loop? (Take \(g=10~\text{m/s}^{2}\), \(\tan 15^{\circ}=0.27\))$$
1. \(1.30\) km
2. \(14.9\) km
3. \(1.55\) km
4. \(20.9\) km

A train runs along an unbanked circular track of radius \(30\) m at a speed of \(54\) km/h. The mass of the train is \(10^{6}\) kg. What is the angle of banking required to prevent wearing out of the rail?

A monkey of mass \(40\) kg climbs on a massless rope (as shown in the figure) which can stand a maximum tension of \(600\) N. In which of the following cases will the rope break?