$A$ ball is released from a height of $10 \, m$. If after the impact there is a loss of $40 \%$ in its energy,the ball shall rise up to ................. $m$.

The friction coefficient between the horizontal surface and each of the blocks shown in the figure is $\mu = 0.2$. The collision between the blocks is perfectly elastic. What is the separation between the blocks when they come to rest? (in $cm$)

$A$ section of a fixed smooth circular track of radius $R$ in a vertical plane is shown in the figure. $A$ block is released from position $A$ and leaves the track at $B$. The radius of curvature of its trajectory when it just leaves the track at $B$ is:

$A$ $15 \,g$ ball is shot from a spring gun whose spring has a force constant of $600 \,N/m$. The spring is compressed by $5 \,cm$. The greatest possible horizontal range of the ball for this compression is .... $m$ $(g = 10 \,m/s^2)$ (in $.0$)

It is well known that a raindrop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop but is otherwise undetermined. Consider a drop of mass $1.00 \; g$ falling from a height $1.00 \; km$. It hits the ground with a speed of $50.0 \; m s^{-1}$. $(a)$ What is the work done by the gravitational force? $(b)$ What is the work done by the unknown resistive force?

Two statements are given below. Select the option that correctly explains both statements.
Statement-$1$: In a perfectly elastic collision between two particles moving in the same direction,they do not lose all their energy.
Statement-$2$: The principle of conservation of momentum is valid for all types of collisions.