Question

A water barrel stands on a table of height $h$. If a small hole is punched in the side of the barrel at its base, it is found that the resultant stream of water strikes the ground at a horizontal distance $R$ from the barrel. The depth of water in the barrel is

• A. $\frac{R}{2}$
• B. $\frac{R^2}{4h}$
• C. $\frac{R^2}{h}$
• D. $\frac{h}{2}$

Answer 1

The correct option is B $\frac{R^2}{4h}$

From TorrIcelli's theorem

$v=\sqrt{2gd}$ ... (i)

where $v$ is horizontal velocity and d is the depth of water in barrel.

Time t to hit the ground is given by

$h=\frac{1}{2}g{t}^{2}ort=\sqrt{\frac{2h}{g}}$
Using equation (i):

$\therefore R=vt=\sqrt{\left(2gd\right)}\sqrt{\frac{2h}{g}}=2\sqrt{dh}$

$\therefore R^2=4dhord=\frac{R^2}{4h}$