Question

A cylinder containing water, stands on a table of height $H$. A small hole is punched in the side of cylinder at its base. The stream of water strikes the ground at a horizontal distance $R$ from the table. Then the depth of water in the cylinder is

• A. $H$
• B. $R$
• C. $\sqrt{R H}$
• D. $R^{2} / 4H$

Answer 1

Answer: (D)

Let depth of water in cylinder be $x$
So velocity $(v)$ of efflux $=\sqrt{2 g x}$
Time taken $(t)$ by water to travel vertical distance of $H$
$=\sqrt{\frac{2 H}{g}}$
$\Rightarrow $ Range $=v \times t$
$R=\sqrt{2 g x} \times \sqrt{\frac{2 H}{g}}$
Solving this we get
$\frac{R^{2}}{4 H}= x$