First slide

Power

Question

If two persons A and B take 2 s and 4 s respectively to lift an object to the same height h, then the ratio of their powers is [Kerala CEE 2014)

Moderate

A

1:2
B

1:1
C

2:1
D

1:3

Solution

Given, $t_{1} = 2 s, t_{2} = 4 s and h_{1} = h_{2} = h$
As, $P_{A} = \frac{m g h_{1}}{t_{1}}$ …(i)
and $P_{B} = \frac{m g h_{2}}{t_{2}}$ …(ii)
On dividing Eq. (i) by Eq. (ii), we get
$P_{A} : P_{B} = \frac{m g h_{1} / t_{1}}{m g h_{2} / t_{2}} = (\frac{h_{1}}{h_{2}}) (\frac{t_{2}}{t_{1}}) = \frac{t_{2}}{t_{1}} = \frac{4}{2} = \frac{2}{1} (∵ h_{1} = h_{2})$
$\Rightarrow P_{A} : P_{B} = 2 : 1$

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