A water barrel having water upto a depth $d$ is placed on a table of height $h$. A small hole is made on the…
A water barrel having water upto a depth $d$ is placed on a table of height $h$. A small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance $R$ from the barrel, then the value of $d$ is
$\frac{4 h}{R^2}$
$4 h R^2$
$\frac{R^2}{4 h}$
$\frac{h}{4 R^2}$
Solution
Velocity of efflux of liquid $v=\sqrt{2 g d}$ Vertical height fall by the liquid $=h$ $\therefore$ Time taken by the liquid $t=\frac{\sqrt{2 h}}{g}$
$\therefore$ Horizontal range $=$ velocity $\times$ time
$
\begin{aligned}
R & =\sqrt{2 g d} \times \frac{\sqrt{2 h}}{g} \\
R^2 & =2 g d \times \frac{2 h}{g} \\
R^2 & =4 d h \\
\Rightarrow \quad d & =\frac{R^2}{4 h}
\end{aligned}
$