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. $1.5H$
• D. $2H$

Answer 1

The correct option is C $1.5H$

Time taken by liquid drops to fall.

$t=\sqrt{\frac{2\left(x\right)}{g}}$

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

Now,

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

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

Now,

for range to be maximum.

$\frac{d\left(R\right)}{dx}=0$

$\Rightarrow \frac{2(3H-2x)}{2\sqrt{x(3H-x)}}=0$

$\Rightarrow x=\frac{3H}{2}$