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:-

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) xm=3 h (B) xm=1.5 h (C) y=h (D) y =0.75 h

Tardigrade Admin · Accepted Answer

For maximum range of y = h <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/6cfff7e0c4afad2d9fc93fecc3b95272-.png" /> V ℓ=√2 g y R = V x T T =√(2(2 H - y )/ g ) R =√4 y (2 H - y ) For maximum range ( dR / dy )=0 on solving y = H R =√4 H (2 H - H )=2 H

Q. 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:-

$x_{m} = 3 h$

$x_{m} = 1.5 h$

$y = h$

$y = 0.75 h$

For maximum range of $y = h$

$V_{ℓ} = 2 g y$
$R = V_{x} T$
$T = \frac{2 ( 2 H - y )}{g}$
$R = 4 y (2 H - y)$
For maximum range
$\frac{d R}{d y} = 0$ on solving $y = H$
$R = 4 H (2 H - H) = 2 H$

Q. 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 xm​ a small hole is punched at a distance of y from the free surface of the liquid. Then:-

xm​=3h

xm​=1.5h

y=h

y=0.75h