A boy weighing 40 kgf climbs up a stair of 30 steps each 20 cm high in 4 minute and a girl weighing 30 kgf does the same in 3 minutes. Compare :-
(i) The work done by them.
(ii) The power developed by them.
Show SolutionHide Solution↓
(i) The work done by them = ?
While climbing both the girl and boy have to do work against the force of gravity.
Force of gravity on boy = F1 = m1g = 40 x 10 = 400
Force of gravity on girl = F2 = m2g = 30 x 10 = 300
Total height climbed up
h = number of steps x height of each step
= 30 x 20 = 600 cm = 6 m
Work done by the boy = W1 = F1 x h = 400 x 6 = 2400 J
Work done by the girl = W2 = F2 x h = 300 x 6 = 1800 J
Therefore, W1 : W2 = 2400 : 1800 = 4 : 3
(ii) The power developed by them = ?
$$\begin{aligned}\frac{P_1}{P_2} = \frac{\frac{W_1}{t_1}}{{\frac{W_2}{t_2}}} \\[0.5em] = \frac{W_1}{W_2} \times \frac{t_2}{t_1} \\[0.5em] = \frac{4}{3} \times \frac{3}{4} \\[0.5em] = 1 : 1\end{aligned}$$