The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 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 kg and the mass of the driver is 65 kg.)
1. \(7.1 \times 10^4 \mathrm{~N}\)
2. \(2.1 \times 10^4 \mathrm{~N}\)
3. \(1.7 \times 10^3 \mathrm{~N}\)
4. \(1.2 \times 10^3 \mathrm{~N}\)

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 \(4\) kg. What is the force on the particle for \(t>4\) s?  (Consider one-dimensional motion only).

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

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 shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m/s, what is the recoil speed of the gun?
1. \(1.2 \mathrm{~cm} \mathrm{~s}^{-1}\)
2. \(2.2 \mathrm{~cm} \mathrm{~s}^{-1}\)
3. \(2.0 \mathrm{~cm} \mathrm{~s}^{-1}\)
4. \(1.6 \mathrm{~cm} \mathrm{~s}^{-1}\)

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 stone of mass \(\mathrm{m}\) tied to the end of a string revolves in a vertical circle of radius \(\mathrm{R}.\) The net forces at the lowest and highest points of the circle directed vertically downwards are:

(${\mathrm{T}}_1$ and ${\mathrm{v}}_1$ denote the tension and speed at the lowest point.${\mathrm{T}}_2$ and ${\mathrm{v}}_2$ 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:

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