$(a)$ 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 $10 \, h$?

(A) Law of conservation of energy: It states that energy can neither be created nor destroyed; it can only be converted from one form to another. The total energy in an isolated system remains constant.
Example: During the free fall of an object,the potential energy is gradually converted into kinetic energy,but the total mechanical energy remains constant.
$(b)$ $(i)$ Power expended by Girl $A$:
Weight $(mg) = 400 \, N$,Height $(h) = 8 \, m$,Time $(t) = 20 \, s$.
Power $(P) = \frac{\text{Work done}}{\text{Time}} = \frac{mgh}{t} = \frac{400 \times 8}{20} = 160 \, W$.
$(ii)$ Power expended by Girl $B$:
Weight $(mg) = 400 \, N$,Height $(h) = 8 \, m$,Time $(t) = 50 \, s$.
Power $(P) = \frac{mgh}{t} = \frac{400 \times 8}{50} = 64 \, W$.
$(c)$ Power $(P) = 1500 \, W = 1.5 \, kW$,Time $(t) = 10 \, h$.
Energy consumed $= P \times t = 1.5 \, kW \times 10 \, h = 15 \, kWh$.