Question

There is hole of area $a$ at the bottom of a cylindrical container of cross-sectional area $A$. Water is filled upto a height of $H$ and all the water flows out in time $t$. If water is filled upto a height of $4H$, all the water will flow out in time -

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

Answer 1

The correct option is B $2t$

We know that, time taken by a tank to empty is given by,
$t=\frac{A}{a}\sqrt{\frac{2H}{g}}$


$\Rightarrow t\propto \sqrt{H}$
$[$ area of hole and cross-sectional area of container is fixed $]$
So, if water is filled upto a height of $4H$, then time taken by tank to empty will be $2t$.