Question

A tank is filled upto a height $h$ with a liquid and is placed on a platform of height $h$ fromt he ground To get maximum range $x _{ m }$ a small hole is punched at a distance of $y$ from the free surface of the liquid. Then:-

• A. $x_{m}=3 h$
• B. $x_{m}=1.5 h$
• C. $y=h$
• D. $y =0.75 h$

Answer 1

Answer: (C)

For maximum range of $y = h$

$ V _{\ell}=\sqrt{2 g y } $
$R = V _{ x } T $
$ T =\sqrt{\frac{2(2 H - y )}{ g }} $
$ R =\sqrt{4 y (2 H - y )}$
For maximum range
$\frac{ dR }{ dy }=0$ on solving $y = H$
$R =\sqrt{4 H (2 H - H )}=2 H$