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A crane 'A' lifts a heavy load in 5 seconds, whereas another crane 'B' does the same work in 2 seconds. Compare the power of crane 'A' to that of crane 'B'.

Machines

ICSE 2020

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Answer

Let the work done by both cranes be 'W'

Given,

Time taken by crane A to do work, t1 = 5 s

Time taken by crane B to do work, t2 = 2 s

Power of crane A, PA = Wt1\dfrac{W}{t_1}

Power of crane B, PB = Wt2\dfrac{W}{t_2}

PAPB=Wt2Wt1PAPB=t2t1PAPB=25\dfrac{PA}{PB} = \dfrac{Wt2}{Wt1} \\[0.5em] \dfrac{PA}{PB} = \dfrac{t2}{t1} \\[0.5em] \dfrac{PA}{PB} = \dfrac{2}{5}

PA : PB = 2 : 5

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