A tank is filled with water up to a height `H`. Water is allowed to come out of a hole `P` in one of the walls at a depth `D` below the surface of water. Express the horizontal distance `x` in terms of `H` and `D`
.

Options

A. `(H)/(2)`
B. `(sqrt3H)/(2)`
C. H
D. None of these

Answer

C

Explanation

speed of efflux `xxu=sqrt(2gh)`
`therefore"Range"x =u sqrt((2(H-h))/(g))`
`x=sqrt(2gh)sqrt((2(H-h))/(g))`
`x^(2)=4(H-h)h=4[Hh-h^(2)]`
`(dx^(2))/(dh)=4[H-2h]=0`
`rArrh=H//2`
`thereforex_(max)=sqrt(2gxx(H)/(2))sqrt((2(H-H//2))/(g))`
= H