The driver of a three-wheeler moving with a speed of \(36~\text{km/h}\) sees a child standing in the middle of the road and brings his vehicle to rest in \(4.0~\text{s}\) just in time to save the child. What is the average retarding force on the vehicle?
(The mass of the three-wheeler is \(400~\text{kg}\) and the mass of the driver is \(65~\text{kg}\).)
1. \(7.1 \times 10^4 ~\text{N}\)
2. \(2.1 \times 10^4 ~\text{N}\)
3. \(1.7 \times 10^3 ~\text{N}\)
4. \(1.2 \times 10^3 ~\text{N}\)

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillations. The speed of the bob at its mean position is $1 m{s}^{-1}$. What is the trajectory of the bob if the string is cut when the bob is at its mean position?

1. Parabolic path
2. elliptical path
3. circular path
4. Straight-line path

A man of mass 70 kg stands on a weighing scale in a lift that is moving. What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?

1. 105 kg
2. 70 kg
3. 0
4. 10 kg

 

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).

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

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)