Question

$10$ min are taken to empty a rectangular vessel of height $h$ through an orifice in its bottom. How much time will it take to be emptied the vessel when half filled?

• A. $3min$
• B. $5min$
• C. $7min$
• D. $9min$

Answer 1

Answer: (C)

$7min$

Time taken to empty a vessel of height $h$, $t=\sqrt{\frac{2h}{g}}$
$\therefore$ Time taken in emptying a vessel of height
$\frac{h}{2},t^{\prime }=\sqrt{\frac{2h/2}{g}}$
$=\sqrt{\frac{h}{g}}$
$\therefore \frac{t^{\prime }}{t}=\frac{1}{\sqrt{2}}$
$t^{\prime }=\frac{t}{\sqrt{2}}=\frac{10}{\sqrt{2}}=7min$.