A large open tank has two holes in the wall. One is a square hole of side L at a depth h from the top and the other is a circular hole of radius R at a depth 4h from the top. When the tank is completely filled with water, quantities of water flowing out per second from both holes are the same. Then R is equal to

Options

A. `L//sqrt(2pi)`
B. `2piL`
C. `L`
D. `1//2pi`

Answer

A

Explanation

Equating the rate of flow, we have
`sqrt((2gy))xxL^(2)=sqrt((2gxx4y))piR^(2)`
`impliesL^(2)=2piR^(2)impliesR=L/sqrt((2pi))`
Flow `=("area")xx("velocity")`. Here `Vel=sqrt(2gx)`
where `x=ht` from top