$A$ ball is dropped from a height of $10 \, m$. If the energy of the ball reduces by $40 \%$ after striking the ground,how much high can the ball bounce back (in $, m$)? $(g = 10 \, m s^{-2})$

Avinash can run with a speed of $8 \, m \, s^{-1}$ against a frictional force of $10 \, N$,and Kapil can move with a speed of $3 \, m \, s^{-1}$ against a frictional force of $25 \, N$. Who is more powerful and why?

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?

State whether the following statement is true or false:
$A$ force does not work, if it produces no motion.

$(a)$ State the law of conservation of energy.
$(b)$ Establish the relation between the $SI$ unit of energy and the commercial unit of energy.
$(c)$ $A$ toy car is displaced through $5 \, m$ on the application of a force of $7 \, N$. Assuming the force acts on the object throughout the displacement,what is the work done in this case?

$A$ 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. $(g = 9.8 \, m s^{-2})$