Question

A tank is filled with water and two holes $A$ and $B$ are made in it. For getting same range, ratio of $\frac{h^{\prime }}{h}$ is

• A. $1:2$
• B. $1:1$
• C. $2:1$
• D. $3:2$

Answer 1

The correct option is B $1:1$


Let the gap between the hole $A$ and hole $B$ is $x$
For hole $A$,
Velocity of efflux $=\sqrt{2g(x+h^{\prime })}$
Range $R=2\sqrt{h(x+h^{\prime })}.....\left(1\right)$
For hole $B$,
Velocity of efflux =$\sqrt{2g{h}^{\prime }}$
Range, $R=2\sqrt{h^{\prime }(x+h)}.....\left(2\right)$
But, range of liquid from hole $A$ and $B$ are equal.
So, from equation $\left(1\right)$ & $\left(2\right)$,
$2\sqrt{h(x+h^{\prime })}=2\sqrt{h^{\prime }(x+h)}$
Squaring on both sides,
$h(x+h^{\prime })=h^{\prime }(x+h)$
$\Rightarrow hx+h{h}^{\prime }=h^{\prime }x+h{h}^{\prime }$
$\Rightarrow h=h^{\prime }$
$\Rightarrow \frac{h^{\prime }}{h}=1$