Question

Water level is maintained in a cylindrical vessel upto a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel, so that the water stream coming out of the hole strikes the horizontal plane of the greatest distance from the vessel?

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

Answer 1

The correct option is A $h=\frac{H}{2}$

Let the height of the hole be $h$, velocity of efflux is $v=\sqrt{2g(H-h)}$, time take to reach the bottom is $\sqrt{\frac{2h}{g}}$.
Then, $x=\sqrt{2g(H-h)}\times \sqrt{\frac{2h}{g}}$, which take maximum value when $h=H/2$.