Question

A boy of mass 40 kg climbs up a flight of 30 steps each of $20cm$ high in 2 minutes and a girl of mass 30 kg does the same in 1.5 minutes. Compare the power developed by them.(Take $g=10m{s}^{-2}$)

• A. 1:1
• B. 4:3
• C. 1:4
• D. 2:3

Answer 1

The correct option is A 1:1

While climbing, both the boy and the girl have to do work against gravity.
Given, mass of the boy, $m_1=40kg$, mass of the girl,$m_2=30kg$, number of steps$=30$, height of each step $=20cm$, time taken by boy, $t_1=2min$, time taken by girl, $t_2=1.5min$ and acceleration due to gravity, $g=10m{s}^{-2}$.
Force of gravity on boy, $F_1=m_{1}g=40\times 10=400N$
Force of gravity on girl, $F_2=m_{2}g=30\times 10=300N$
Total height climbed,$h=numberofsteps\times heightofeachstep\Rightarrow 30\times 20=600cm=6m$ (This height is same for the boy and the girl)
Work done by the boy, $W_1=F_1\times h=400\times 6=2400J$
Work done by the girl, $W_2=F_2\times h=300\times 6=1800J$
$\therefore$ $W_1:W_2=2400:1800=4:3$.
$\frac{\text{Power developed by girl}}{\text{Power developed by boy}}=\frac{\frac{W_1}{t_1}}{\frac{W_2}{t_2}}=\frac{W_1}{W_2}\times \frac{t_2}{t_1}\Rightarrow \frac{4}{3}\times \frac{1.5}{2}=1:1$
Therefore, the power developed is the same for the boy and girl.