Find the velocity of a body of mass $100 \, g$ having a kinetic energy of $20 \, J$. (in $, m s^{-1}$)

What happens to the kinetic energy when
$(i)$ the mass of the body is doubled at constant velocity?
$(ii)$ the velocity of the body is doubled at constant mass?
$(iii)$ the mass of the body is doubled but the velocity is reduced to half?

$(a)$ Can a body have energy without having momentum? Explain.
$(b)$ Can a body have momentum without having energy? Explain.

$A$ mass of $10 \, kg$ is dropped from a height of $50 \, cm$. Find its:
$(a)$ Potential energy just before dropping.
$(b)$ Kinetic energy just on touching the ground.
$(c)$ Velocity with which it hits the ground. (Given: $g = 10 \, m s^{-2}$)

$(a)$ Define power. Give its $SI$ unit.
$(b)$ Taking the example of a simple pendulum, explain the variations in the forms of energy and the interconversions involved.

$A$ boy of mass $40 \, kg$ runs up a flight of $50$ steps,each $10 \, cm$ high,in $5 \, s$. Find: $(i)$ the work done by the boy,and $(ii)$ the power developed. $(g = 9.8 \, m s^{-2})$