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

Options

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

Answer

A

Explanation

`A_(1)v_(1)=A_(2)v_(2) " or " A_(1)=sqrt(2gh_(2))=A_(2)sqrt(2gh)`
or ` A_(1)^(2)h_(1)=A_(2)^(2)h_(2) implies (L^(2))^(2) (y)=(pi R^(2))^(2)(4y)`
or `R=(L)/(sqrt(2pi))`