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Water in a tank is filled to a depth H whose side walls are vertical. A hole is made on one of the walls at a depth h below the free surface of water. If R is the distance at which the stream strikes the ground, then

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$R = \sqrt{2 h (H - h)}$

$R = 2 \sqrt{H (H - h)}$

$R = 2 \sqrt{h (H - h)}$

$R = 2 \sqrt{hH}$

answer is D.

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Detailed Solution

Velocity of efflux at depth h below free surface. $v = \sqrt{2 gh}$ (In horizontal direction) time taken by liquid to fall from (H–h) height under gravity $t = \sqrt{\frac{2 (H - h)}{g}}$

horizontal distance R = vt. $\Rightarrow R = \sqrt{2 g h} \times \sqrt{\frac{2 (H - h)}{g}} \Rightarrow R = 2 \sqrt{h (H - h)}$

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