Calculate the power of a motor which is capable of raising $1000 k g$ of water in $5$ minutes from a well $60 m$ deep. $g = 9.8 m / s^{2}$ .

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Solution

Given that,

Mass of the water to be raised $m = 1000 k g$

Height through which it will be raised $h = 60 m$

Acceleration due to gravity $g = 9.8 m / s^{2}$

Time taken $t = 5 min = 300 s$

Work done in lifting the water

$W = m g h$

$W = 1000 \times 9.8 \times 60$

$W = 588000 J$

Power is defined as the rate of doing work

$P = \frac{W}{t}$

$P = \frac{588000}{300}$

$P = 1960 W a t t s$
$P = 2.63 h p$

Hence, the power of a motor is $2.63 h p$

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