Question

A tank is filled with water upto a height H. Water is allowed to come out of a hole P in one of the walls at some depth below the surface of water. The maximum horizontal distance $x$ is

• A. $\frac{H}{2}$
• B. $\frac{\sqrt{3}H}{2}$
• C. $H$
• D. None of these

Answer 1

The correct option is C $H$

Speed of efflux, $u=\sqrt{2gh}$
$\therefore Range,x=u\sqrt{\frac{2(H-h)}{g}}$

$x=\sqrt{2gh}\sqrt{\frac{2(H-h)}{g}}$
$x^2=4(H-h)h=4[Hh-h^2]$
$\frac{d\left(x^2\right)}{dh}=4[H-2h]=0$
$\Rightarrow h=H/2$
$\therefore x_{max}=\sqrt{2g\times \frac{H}{2}}\sqrt{\frac{2(H-\frac{H}{2})}{g}}=H$