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Q.

The level of the water in a vessel falls from a height 81cm to 49cm in 5 minutes as water flows through a hole in it’s bottom. What further time is required for the water level to fall from 49 to 25 cm ?

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a

10 minutes

b

5 minutes

c

20 minutes

d

2.5 minutes

answer is B.

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Detailed Solution

$t = \frac{A}{a} \sqrt{\frac{2}{g}} (\sqrt{h_{1}} - \sqrt{h_{2}})$

$t \propto \sqrt{h_{1}} - \sqrt{h_{2}} \Rightarrow \frac{t_{1}}{t_{2}} = \frac{\sqrt{h_{1}} - \sqrt{h_{2}}}{\sqrt{h_{1}^{1}} - \sqrt{h_{2}^{1}}} = \frac{\sqrt{81} - \sqrt{49}}{\sqrt{49} - \sqrt{25}} = \frac{9 - 7}{7 - 5} = \frac{2}{2}, t_{2} = t_{1}$

$t_{2} = 5 \min$

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