Question

A cylindrical vessel is filled with water up to height $H$. A hole is bored in the wall at a depth $h$ from the free surface of water. For maximum range, $h$ is equal to :-

• A. $\frac{H}{4}$
• B. $\frac{H}{2}$
• C. $\frac{3H}{4}$
• D. $H$

Answer 1

Answer: (B)

$\frac{H}{2}$

The cylinder is filled upto a height of $H$ and a hole is drilled at a depth h from the surface of water.

This means that the velocity of water flowing out of the hole is $\sqrt{2g(H-h)}$

The time taken for the stream of water to reach ground,

$h=0+0.5g{t}^2$

This gives, $t=\sqrt{h/5}$

The range of this stream would be, $x=ut$

$x=\sqrt{2gh(H-h)/5}$

For maximum $x$, $dx/dh=0$ , which gives $h=H/2$