A bullet of mass \(0.04~\text{kg}\) moving with a speed of \(90~\text{m/s}\) enters a heavy fixed wooden block and is stopped after a distance of \(60~\text{cm}\). The average resistive force exerted by the block on the bullet is:

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. \(2mg\)

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.

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 \(30~\mathrm{N}\)

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