Question

A boy weighing 40kgf climbs up a stair of 30 steps each 20 cm high in 4 minute and a girl weighing 30kgf does the same in 3 minutes. Compare:
(i) The work done by them.
(ii) The power developed by them

Answer 1

(i) Given: $m_1=40kgf,m_2=30kgf,h_1=h_2,t_1=4minutes=4\times 60sec,t_2=3minutes=3\times 60sec$

Comparing work done by them:

$\frac{\text{Work done by a boy}}{\text{Work done by girl}}=\frac{m_{1}g{h}_1}{m_{2}g{h}_2}=\frac{m_1}{m_2}=\frac{40}{30}=4:3$

(ii) Comparing power developed by them:

$\frac{\text{Power developed by boy}}{\text{Power developed by girl}}=\frac{\text{Work done by boy / time taken to climb up the stairs in seconds}}{\text{Work done by girl / time taken to climb up the stairs in seconds}}$

$=\frac{\frac{2400}{4\times 60}}{\frac{1800}{3\times 60}}$

$=\frac{2400}{4\times 60}\times \frac{3\times 60}{1800}=1:1$