$A$ lead bullet penetrates into a solid object and melts. Assuming that $40 \%$ of its kinetic energy is used to heat it,the initial speed of the bullet is ............ $m \, s^{-1}$.
(Given: Initial temperature of the bullet $= 127^{\circ} C$,
Melting point of the bullet $= 327^{\circ} C$,
Latent heat of fusion of lead $= 2.5 \times 10^{4} \, J \, kg^{-1}$,
Specific heat capacity of lead $= 125 \, J \, kg^{-1} K^{-1}$)

Two blocks $A(5 \ kg)$ and $B(2 \ kg)$ attached to the ends of a spring of spring constant $k = 1120 \ N/m$ are placed on a smooth horizontal plane with the spring undeformed. Simultaneously,velocities of $3 \ m/s$ and $10 \ m/s$ along the line of the spring in the same direction are imparted to $A$ and $B$. Then:

$A$ rain drop of radius $2 \; mm$ falls from a height of $500 \; m$ above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height,it attains its maximum (terminal) speed,and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is $10 \; m s^{-1}$?

$A$ pendulum of length $1 \,m$ and having a bob of mass $1 \,g$ is pulled aside through an angle $60^{\circ}$ with the vertical and then released. The power delivered by all the forces acting on the bob when the pendulum makes $30^{\circ}$ with the vertical is . . . . . . $\left(g=10 \,ms^{-2}\right)$ (in $\,mW$)

Given below are two statements:
Statement $I$: $A$ truck and a car moving with the same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.
Statement $II$: $A$ car moving towards the east takes a turn and moves towards the north, the speed remains unchanged. The acceleration of the car is zero.
In the light of the given statements, choose the most appropriate answer from the options given below.

Two persons $A$ and $B$ are throwing a ball of mass $200 \ g$ at a wall as shown in the figure. The balls strike the wall perpendicularly at the same point at a height of $2 \ m$ from the ground. The balls strike the wall elastically at the same time and return back to $A$ and $B$ at the same time. They repeat this process. What is the average force exerted on the wall (in $N$)? (Take $g = 10 \ m/s^2$)