A tank on the roof of a $20$ m high building can hold $10 m^{3}$ of water. The tank is to be filled from a pond on the ground in $20$ minutes. If the pump has an efficiency of $60$ %, the input power required is

1.1 k W

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2.72 k W

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5.48 k W

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7.0 k W

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Solution

The correct option is A $2.72 k W$
$1 m^{3}$ of water is $1000 L$ and weigh $1000 k g$ .
So, the weight of $10 m^{3}$ is $10000 k g$ .
So, mass $m = 10000 k g$
Height, $h = 20 m$
Gravitational acceleration, $g = 9.8 m / s^{2}$
Time, $t = 20 \times 60 s e c$
Since efficiency of the pump is $60$ %, we can write that,
$\frac{60 P}{100} = \frac{m g h}{t}$
$P = \frac{10000 \times 9.8 \times 20 \times 100}{60 \times 20 \times 60} = 2.72 k W$

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