Question

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

• A. $3:4$
• B. $4:3$
• C. $1:1$
• D. $3:2$

Answer 1

The correct option is B $4:3$

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, $t_2=2min$ and acceleration due to gravity, $g=10m{s}^{-2}$.

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, $W_1=m_1\times g\times h=40\times 10\times 6$
$=2400J$
Work done by the girl, $W_2=m_2\times g\times h=30\times 10\times 6$
$=1800J$
$\therefore$ $W_1:W_2=2400:1800=4:3$.
$\frac{\text{Power developed by girl}}{\text{Power developed by boy}}=\frac{\frac{W_1}{t_1}}{\frac{W_2}{t_2}}=\frac{W_1}{W_2}\times \frac{t_2}{t_1}\Rightarrow \frac{4}{3}\times \frac{2}{2}=4:3$
Therefore, the power developed for the boy and girl is in ratio of $4:3$.