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A water barrel having water up to a depth $d$ is placed on a table of height $h$ . A small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel, then the value of $d$ is:

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$4 h R^{2}$

$\frac{h}{4 R^{2}}$

$\frac{R^{2}}{4 h}$

$\frac{4 h}{R^{2}}$

answer is C.

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Detailed Solution

Velocity of efflux, $v = \sqrt{2 g d}$

Time taken for the range, $R = \sqrt{\frac{2 h}{g}}$

$Range = velocity \times time$

$R = \sqrt{2 g d} \times \sqrt{\frac{2 h}{g}}$

or $R^{2} = 2 d g \times \frac{2 h}{g} = 4 d h$

$∴$ $d = \frac{R^{2}}{4 h}$

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