Question

A tank is filled upto height $L$ with a liquid and is placed on a platform of height $h$ from the 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. $x_m=2h$
• B. $x_m=1.5h$
• C. $y=h$
• D. $y=0.75h$

Answer 1

Answer: (A), (C)

The correct options are
A $x_m=2h$
C $y=h$

Velocity of efflux at y $V_x=\sqrt{2gy}$
At y, vertical component is zero
The distance to ground is $h=(L-y)$ if L is the distance from ground to top of vessel
Hence, time required to reach ground $t=\sqrt{2(L-y)/g}$
Horizontal Range is $V_x\times t$
As we have to maximize range, we differentiate $V_{x}t$ with $y$
We get range maximum for $y=L/2=h$
Accordingly, if we put $y=h$ in range equation, we get range $=2h$