A rectangular vessel when full of water takes 10 minutes to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water

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9 minute

7 minute

5 minute

3 minute

answer is B.

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Detailed Solution

Time taken to be emptied for h height, $t = \sqrt{\frac{2 h}{g}}$

and for $\frac{h}{2}$ height, $t' = \sqrt{\frac{2 h / 2}{g}} = \sqrt{\frac{h}{g}}$

$∴ \frac{t^{'}}{t} = \frac{1}{\sqrt{2}} \Rightarrow t^{'} = \frac{t}{\sqrt{2}} = \frac{10}{\sqrt{2}} = 7 minute$

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