The time taken by an engine of power $10 kW$ to lift a mass of $200 kg$ to a height of $40 m$ is $(g = 10 m s^{- 2})$

2 s

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4 s

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8 s

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16 s

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Solution

The correct option is C $8 s$
Given, mass of a body = $200 k g$
height $h = 40 m$
Power $(P) = \frac{W}{t}$
under the pressure of a conservative force (gravity) work done against gravity
$- W = U_{1} - U_{2}$
$\Rightarrow W = U_{2} - U_{1} = m g h$
$∴ P = \frac{m g h}{t}$
$\Rightarrow t = \frac{m g h}{p} = \frac{200 \times 10 \times 40}{10 \times 10^{3}} = 8 s$

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