$(a)$ 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.

$(a)$ Is it possible that a body is in accelerated motion under the action of a force,yet no work is being done by the force? Explain with an example.
$(b)$ Two bodies of masses $m_{1}$ and $m_{2}$ have equal kinetic energies. What is the ratio of their linear momenta?

$A$ man of mass $60 \, kg$ runs up a flight of $30$ steps in $40 \, s$. If each step is $20 \, cm$ high,calculate the power of the man.

State whether the following statement is true or false:
When energy changes from one form to another,the energy that disappears from one form reappears in an exactly equivalent amount in the other form.

$(a)$ State the law of conservation of energy. Explain it with one example.
$(b)$ Two girls,each of weight $400 \, N$,climb up a rope to a height of $8 \, m$. Girl $A$ takes $20 \, s$ while Girl $B$ takes $50 \, s$ to accomplish the task. What is the power expended by each girl?
$(c)$ An electric heater is rated $1500 \, W$. How much energy does it use in $10 \, h$?

Identify the kind of energy possessed by a running athlete.