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  4. Two men with weights in the ratio 4:3 run up a staircase in time in the ratio 12:11 . The ratio of the power of the first to that of second is

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Q. Two men with weights in the ratio $4:3$ run up a staircase in time in the ratio $12:11$ . The ratio of the power of the first to that of second is

NTA AbhyasNTA Abhyas 2022

Solution:

$\text{Power}=\frac{\text{work}}{\text{time}}=\frac{\text{energy}}{\text{time}}=\frac{\textit{mgh}}{t}=\frac{W h ⁡}{t}$ ( $W$ = weight )
$\therefore \frac{P _{1}}{P ⁡_{2}}=\frac{W ⁡_{1}}{W ⁡_{2}}\times \frac{t_{2}}{t_{1}}=\frac{4}{3}\times \frac{1 1}{1 2}=\frac{1 1}{9}$ ( $h$ is same in both cases )