Question

The height of water level in a tank is $H$. The range of water stream coming out of a hole at depth $\frac{H}{4}$ from upper water level will be.

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

Answer 1

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

The horizontal range of the liquid coming out a hole is equal to $2\sqrt{h{h}^{\prime }}$, 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

Here, $h=\frac{H}{4}$ and $h^{\prime }=H-\frac{H}{4}=\frac{3H}{4}$

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