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Q.

There is a hole at the bottom of a large vessel open at the top. If water is filled up to a height h, it flows out in time t. if water is filled to a height 2h, it will flow out in time

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a

$\sqrt{2} t$

b

2t

c

$2 \sqrt{2} t$

d

4t

answer is A.

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Detailed Solution

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Use the formula $t = \frac{A}{a} \sqrt{\frac{2}{g}} [\sqrt{H_{1}} - \sqrt{H_{2}}]$ In the first case, $H_{1} = h, H_{2} = 0$ Therefore, $t = \frac{A}{a} \sqrt{\frac{2}{g}} [\sqrt{h} - 0]$ In the second case, $H_{1} = 2 h, H_{2} = 0$ . Therefore, $t^{'} = \frac{A}{a} \sqrt{\frac{2}{g}} [\sqrt{2 h} - 0] \Rightarrow \frac{t^{'}}{t} = \sqrt{2}$

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