The ratio of powers of two motors is , that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of will be [2023]

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Solution

Q.
The ratio of powers of two motors is $\frac{3 \sqrt{x}}{\sqrt{x} + 1}$ , that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of $x$ will be [2023]

1 2

2 4

3 2.4

4 16

Ans.
(4)

$Average Power = \frac{total work done}{total time} = \frac{m g h}{t}$

$\frac{P_{1}}{P_{2}} = \frac{\frac{m_{1} g h}{t_{1}}}{\frac{m_{2} g h}{t_{2}}} = \frac{m_{1}}{t_{1}} \frac{t_{2}}{m_{2}}$

$\frac{P_{1}}{P_{2}} = \frac{300 \times 2}{5 \times 50} = \frac{12}{5} = \frac{3 \sqrt{x}}{\sqrt{x} + 1}$

$\Rightarrow x = 16$

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