A circular racetrack of radius \(300~\text m\) is banked at an angle of \(15^\circ.\) If the coefficient of friction between the wheels of a race-car and the road is \(0.2,\) what is the (a) optimum speed of the race-car to avoid wear and tear on its tyres, and (b) maximum permissible speed to avoid slipping?

1.	\(v_0=28.1\) m/s and \(v_{max}=38.1\) m/s
2.	\(v_0=38.1\) m/s and \(v_{max}=28.1\) m/s
3.	\(v_0=0\) m/s and \(v_{max}=28.1\) m/s
4.	\(v_0=38.1\) m/s and \(v_{max}=100\) m/s

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

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 direction of the force on the wall due to ball in case (a) and (b) respectively is in the direction of?

            

1.	+ve x-axis & –ve x-axis	2.	–ve x-axis & +ve y-axis
3.	+ve x-axis in both cases	4.	–ve x-axis in both cases

The figure shows the position-time graph of a body of mass 0.04 kg. What is the time between two consecutive impulses received by the body? 

1. 2 s

2. 4 s

3. 1 s

4. 3 s

Figure shows the position-time graph of a body of mass 0.04 kg. What is the magnitude of each impulse recieved by the  body?

1. $8\times {10}^{-4} kg-m/s$

2. $2\times {10}^{-4} kg-m/s$

3. $4\times {10}^{-4} kg-m/s$

4. $6\times {10}^{-4} kg-m/s$

A ball of mass \(0.15~\text{kg}\) is dropped from a height \(10~\text{m}\), strikes the ground, and rebounds to the same height. The magnitude of impulse imparted to the ball is \((g=10 ~\text{m}/\text{s}^2)\) nearly:
1. \(2.1~\text{kg-m/s}\)
2. \(1.4~\text{kg-m/s}\)
3. \(0~\text{kg-m/s}\)
4. \(4.2~\text{kg-m/s}\)

A cyclist speeding at 18 km/h on a level road takes a sharp circular turn of radius 3 m without reducing the speed. The coefficient of static friction between the tyres and the road is 0.1. Will the cyclist slip while taking the turn?

What is the acceleration of the block and tension in the string of the block and trolley system shown in a figure, if the coefficient of kinetic friction between the trolley and the surface is \(0.04\)?
Take \(g=10~\mathrm{m/s^2}\)${\mathrm{}}^{}$  and neglect the mass of the string.
                    
1. \(9.6~\mathrm{m/s^2}\) and \(27.1~\mathrm{N}\)
2. \(9.6~\mathrm{m/s^2}\) and \(2.71~\mathrm{N}\)
3. \(0.96~\mathrm{m/s^2}\) and \(27.1~\mathrm{N}\)
4. \(0.63~\mathrm{m/s^2}\) and \(30~\mathrm{N}\)

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?

  
1. \(0.27\)
2. \(0.53\)
3. \(0.23\)
4. \(0.25\)