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.)

$$\begin{gathered} \left(1\right) 7.1\times {10}^4 N \\ \left(2\right) 2.1\times {10}^4 N \\ \left(3\right) 1.7\times {10}^3 N \\ \left(4\right) 1.2\times {10}^3 N \end{gathered}$$

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?

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?

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).

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?

$$\begin{gathered} \left(1\right) 0.4 kg m s^{-1} \\ \left(2\right) 0.3 kg m s^{-1} \\ \left(3\right) 0.6 kg m s^{-1} \\ \left(4\right) 0.7 kg m s^{-1} \end{gathered}$$

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:

A stone of mass m tied to the end of a string revolves in a vertical circle of radius 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:

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

A stream of water flowing horizontally with a speed of $15 m s^{-1}$ pushes out of a tube of cross-sectional area ${10}^{-2} m^2$ and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound?

An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15°. What is the radius of the loop? $[\tan {15}^o=0.27]$

A train runs along an unbanked circular track of a radius of 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?

$$\begin{gathered} \left(1\right) {30}^0 \\ \left(2\right) {45}^0 \\ \left(3\right) {53}^0 \\ \left(4\right) {37}^0 \end{gathered}$$

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? 

A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 revs/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?

A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of $4 {\mathrm{ms}}^{-1}$ relative to the trolley in a direction opposite to its motion, and jumps out of the trolley. What is the final speed of the trolley?

A particle of mass 200 g is moving in a circle of radius 2 m. The particle is just 'looping the loop'. The speed of the particle and the tension in the string at highest point of the circular path are (g=10 ms^-2)

A particle of mass 200 g, is whirled into a vertical circle of radius 80 cm using a massless string. The speed of the particle when the string makes an angle of $60°$ with the vertical line is 1.5 ms^-1. The tension in the string at this position is

A string tied on a roof bears a maximum tension of 50 kg-wt. The minimum acceleration that can be acquired by a man of 98 kg to descend will be:
[Take g=9.8 m/s²]

A balloon has 2 g of air. A small hole is pierced into it. The air comes out with a velocity of 4 m/s. If the balloon shrinks completely in 2.5 s, the average force acting on the balloon is:

In a cricket match, the fielder draws his hands backward after receiving the ball in order to take a catch because:

A body is placed on a rough inclined plane of inclination $\mathrm{\theta }$. As the angle $\mathrm{\theta }$ is increased from 0^o to 90^o , the contact force between the block and the plane

Q. 1 A ball is traveling with uniform translatory motion. This means that

Q. 2 A meter scale is moving with uniform velocity. This implies

Q.3 A cricket ball of mass 150 g has an initial velocity $\mathrm{u}=(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}){\mathrm{ms}}^{-1}$ and a  final velocity$\mathrm{v}=-(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}){\mathrm{ms}}^{-1}$, after being hit. The change in momentum (final momentum-initial momentum) is (in kgm/s)

Q. 5 Conservation of momentum in a collision between particles can be understood from

Q. 6 A hockey player is moving northward and suddenly turns westward at the same speed to avoid an opponent. The force that acts on the player is

Q. 7 A body of mass 2kg travels according to the law$\mathrm{x}\left(\mathrm{t}\right)=\mathrm{pt}+{\mathrm{qt}}^2+{\mathrm{rt}}^3$ where, $\mathrm{q}=4{\mathrm{ms}}^{-2},\mathrm{p}=3{\mathrm{ms}}^{-1}\text{ and }\mathrm{r}=5{\mathrm{ms}}^{-3}$. The force acting on the body at t=2s is

Q. 8 A body with a mass 5 kg is acted upon by a force $\mathrm{F}=(-3\hat{\mathrm{i}}+4\hat{\mathrm{j}})\mathrm{N}$. If its initial velocity at t = 0 is $v=(6\hat{i}-12\hat{j})m{s}^{-1}$, the time at which it will just have a velocity along the Y-axis is

Q. 9 A car of mass m starts from rest and acquires a velocity along the east, $\mathrm{v}=\mathrm{v}\hat{\mathrm{i}}(\mathrm{v}>0)$ in two seconds. Assuming the car moves with uniform acceleration, the force exerted on the car is

Q. 11 In the figure the coefficient of friction between the floor and the body B is 0.1. The coefficient of friction between the bodies B and A is 0.2. A force F is applied as shown on B. The mass of A is rn/2 and of B is m. Which of the following statements are true?

(a) The IN)dies will move together if F = O .25 mg
(b) The A will slip with B if F = 0.5 mg
(c) The bodies will move together if F = 0.5 mg
(d) The bodies will be at rest if F = 0.1 mg
(e) The maximum value of F for which the two bodies will move together is 0.45 mg