A man $M_{1}$ of mass $80 k g$ runs up a staircase in $15 s$ . Another man $M_{2}$ also of mass $80 k g$ runs up the stair case in $20 s$ . The ratio of the power developed by them will be:

1

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4 / 3

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16 / 9

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None of the above

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Solution

The correct option is A $4 / 3$
Let the height of the staircase is $h$ .

$Power of the first man: - ----------------------- -$
Work done by the man = $m g h = 80 \times g \times h$
Time taken by the man to ascend the staircase is $15 s$
Power of the man $P_{1} = \frac{m g h}{t} = \frac{80 \times g \times h}{15} W$

$Power of the second man: - -------------------------- -$
Work done by the man = $m g h = 80 \times g \times h$
Time taken by the man to ascend the staircase is $20 s$
Power of the man $P_{2} = \frac{m g h}{t} = \frac{80 \times g \times h}{20} W$

Thus, $\frac{P_{1}}{P_{2}} = \frac{20}{15} = \frac{4}{3}$

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