A cylinderical vessel is filled with water up to height H. A hole is bored in the wall at a depth h from the free surface of water. For maximum range h is equal to

Options

A. `(H)/(4)`
B. `(H)/(2)`
C. `(3H)/(4)`
D. H

Answer

B

Explanation

Velocity of water flowing out of hole, `v= sqrt(2gh)`
Height of hole from ground level `= (H-h)`
The time taken by water to cover vertical distance `(H-h)` is given by `(H- h) = (1)/(2) "gt"^(2) or t= sqrt((2(H-h))/(g))`
Horizontal range will be maximum if `(dR)/(dh) = 0`
i.e. `2 xx (1)/(2) (h H - h^(2))^(-1//2) xx (H - 2h) = 0`
or `H = 2h or h = (H)/(2)`