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

Answer

A

Explanation

`a_(1)v_(1)=a_(2)v_(2)`
`:. (L^2)sqrt(2gh)=(pi R^2)sqrt(2g (4h))`
`R=L/(sqrt(2 pi))`.