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

State whether the following statement is true or false:
Work done by centripetal force is zero.

An iron sphere of mass $30 \, kg$ has the same diameter as an aluminium sphere whose mass is $10.5 \, kg$. The spheres are dropped simultaneously from a cliff. When they are $10 \, m$ from the ground,they have the same:

$(a)$ The Earth,moving around the Sun in a circular orbit,is acted upon by a force,and hence work must be done on the Earth by the force. State whether the statement is correct or not. Give reasons for your answer.
$(b)$ $A$ coolie holding a heavy box is waiting at the bus stand for $15$ minutes. How much work is done by him?
$(c)$ $A$ man weighing $70 \, kg$ carries a weight of $10 \, kg$ to the top of a tower $100 \, m$ high. Calculate the work done by the man. $(g = 10 \, m s^{-2})$

State whether the following statement is true or false:
Kilowatt hour $(kWh)$ is the unit of power.

$(a)$ 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.