Question

The height of the 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

• A. H
• B. $\frac{H}{2}$
• C. $\frac{3H}{2}$
• D. $\frac{\sqrt{3}H}{2}$

Answer 1

The correct option is D $\frac{\sqrt{3}H}{2}$

Given:

$h^{\prime }=\frac{3H}{4}$

$h=H-\frac{3H}{4}=\frac{H}{4}$

horizontal range of the liquid coming out a hole $R=2\sqrt{h{h}^{\prime }}$

where

$h=$ depth of the hole below the free surface of the liquid

$h^{\prime }=$ height of the hole above the bottom of the tank

So, Range of the water stream, $R=2\sqrt{\frac{H}{4}\times \frac{3H}{4}}=\frac{\sqrt{3}H}{2}$