Question

A tank is filled up to a height $2H$ with a liquid and is placed on a platform of height $H$ from the ground.The distance $x$ from the ground where a small hole is punched to get the maximum range $R$ is

• A. $H$
• B. $1.25H$
• C. $1.5$
• D. $2H$

Answer 1

The correct option is C $1.5$

Pressure at a height $x=\rho g(3H-x)$

Using Bernoulli's Equation inside and outside the hole,

$\frac{1}{2}\rho v^2=\rho g(3H-x)$

$⟹v=\sqrt{2(3H-x)g}$

Range of the liquid=$vt=v\sqrt{\frac{2x}{g}}$

$=2\sqrt{x(3H-x)}$

This is maximum for $x=1.5H$