If the body A does a work in 20 s and body B does the same work in 40 s then, what is the ratio of their power respectively?

2:1

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3:2

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3:4

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4:1

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Solution

The correct option is A
2:1

Let the power developed by body A = $P_{A}$ and power developed by body B = $P_{B}$
Given, time taken by A, $t_{A} = 20 s$ and time taken by B, $t_{B} = 40 s$ .
Power, $P = \frac{Work done}{Time taken}$
As work done is constant or same, power is inversely proportional to time taken.
$\Rightarrow$ $\frac{P_{A}}{P_{B}} = \frac{t_{B}}{t_{A}} = \frac{40}{20} = \frac{2}{1}$ .
Hence, power ratio $= 2:1$ .

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