An object of mass $1 \, kg$ has a potential energy of $1 \, J$ relative to the ground when it is at a height of: (in $, m$)

In each of the following cases,a force $F$ is acting on an object of mass $m$. The direction of displacement is from west to east,shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative $(-ve)$,positive $(+ve)$,or zero $(0)$.

The $CGS$ unit of work is:

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

$(i)$ State the law of conservation of energy.
$(ii)$ Show that the total mechanical energy of a freely falling body is conserved.