The height of water in a tank is H. The range | vedclass

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(D) Let $h$ be the depth of the hole from the upper surface,so $h = \frac{3H}{4}$.The height of the water column above the hole is $h = \frac{3H}{4}$,

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$\frac{\sqrt{3}H}{2}$

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(D) Let $h$ be the depth of the hole from the upper surface,so $h = \frac{3H}{4}$.The height of the water column above the hole is $h = \frac{3H}{4}$,and the height of the water column below the hole is $H - h = H - \frac{3H}{4} = \frac{H}{4}$.The velocity of efflux is given by Torricelli's law: $v = \sqrt{2gh} = \sqrt{2g \left(\frac{3H}{4}ight)} = \sqrt{\frac{3gH}{2}}$.The time taken for the liquid to reach the ground is $t = \sqrt{\frac{2(H-h)}{g}} = \sqrt{\frac{2(H/4)}{g}} = \sqrt{\frac{H}{2g}}$.The horizontal range $R$ is given by $R = v 	imes t$.$R = \sqrt{\frac{3gH}{2}} 	imes \sqrt{\frac{H}{2g}} = \sqrt{\frac{3gH^2}{4g}} = \sqrt{\frac{3H^2}{4}} = \frac{\sqrt{3}H}{2}$.

The height of water in a tank is $H$. The range of the liquid emerging out from a hole in the wall of the tank at a depth $\frac{3H}{4}$ from the upper surface of water will be

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