Consider a rubber ball freely falling from a height $h = 4.9\, m$ on a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Which one of the following graphs represents the velocity as a function of time and the height as a function of time?

An engine pumps up $100 \ kg$ of water through a height of $10 \ m$ in $5 \ s$. Given that the efficiency of the engine is $60\%$. If $g = 10 \ m \ s^{-2}$,the power of the engine is .............. $kW$.

Two balls $A$ and $B$ having masses $1\, kg$ and $2\, kg$,moving with speeds $21\, m/s$ and $4\, m/s$ respectively in opposite directions,collide head-on. After the collision,$A$ moves with a speed of $1\, m/s$ in the same direction. Which of the following statements is correct?

$A$ small bucket of mass $M \, kg$ is attached to a non-extensible string of length $L \, m$. The bucket is released from rest when the string is in a horizontal position. At its lowest point,the bucket scoops up $m \, kg$ of water and rises to a height $h$. The height $h$ (in meters) is:

Fill in the blanks:
$(a)$ In electricity consumption,$1$ unit is equal to .......... Joules of work.
$(b)$ $A$ body falling from a height of $10 \ m$ onto hard ground loses $20 \%$ of its energy. It can reach a height of .............
$(c)$ $A$ particle moves in a circular path of radius $a$ under the influence of an attractive force with potential energy $U = -\frac{k}{2r^2}$. Its total energy is = .......
$(d)$ Converting a mass of $1 \ \mu g$ into energy yields ........ energy.

$A$ ball is released from a certain height. It loses $50\%$ of its kinetic energy on striking the ground. It will attain a height again equal to