Question

A water barrel having water up to 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:

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

Answer 1

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

By Bernoulli's equation:

mgd = $\frac{1}{2}m{v}^2$

v = $\sqrt{2gd}$ ....... (1)

By Projectile motion equation:

$\frac{1}{2}g{t}^2=h$

t = $\sqrt{\frac{2h}{g}}$

Therefore, $R=vt$

= $\sqrt{2gd}\sqrt{\frac{2h}{g}}$

= 2 $\sqrt{dh}$

Hence d = $\frac{R^2}{4h}$