The motion of a particle of mass \(m\) is described by \(y=ut+\frac{1}{2}gt^{2}.\)  The force acting on the particle is: 
1. \(3mg\)
2. \(mg\)
3. \(\frac{mg}{2}\)
4. \(2mg\)

A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of \(12\) m/s. If the mass of the ball is \(0.15\) kg, then the impulse imparted to the ball is:
(Assume linear motion of the ball.)
1. \(0.15\) N-s
2. \(3.6\) N-s
3. \(36\) N-s
4. \(0.36\) N-s

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 ratio of the magnitudes of impulses imparted to the balls by the wall is:
      

See the figure given below. A mass of \(6\) kg is suspended by a rope of length \(2\) m from the ceiling. A force of \(50\) N is applied at the mid-point \(P\) of the rope in the horizontal direction, as shown. What angle does the rope make with the vertical in equilibrium? (Take \(g=10~\text{ms}^{-2}\)). Neglect the mass of the rope.

See the figure given below, a mass of \(4~\text{kg}\) 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. \(0.25\)

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 \(30~\mathrm{N}\)

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?

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?

In the figure given below, a wooden block of mass \(2~\text{kg}\) rests on a soft horizontal floor. When an iron cylinder of mass \(25~\text{kg}\) is placed on top of the block, the floor yields steadily and the block and the cylinder together go down with an acceleration of \(0.1~\text{m/s}^{2}.\) What is the force of the block on the floor after the floor yields?
(take \(g=10~\text{m/s}^{2}\)${\mathrm{}}^{}$)
     
1. \(270~\text{N}\) upward
2. \(267.3~\text{N}\) downward
3. \(20~\text{N}\) downward
4. \(267.3~\text{N}\) upward