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

Explanation

Velocity of efflux at a depth h is given
by `v=sqrt(2gh)`.
Volume of water flowing out per second from both the holes are equal
`because a_(1)v_(1)=a_(2)v_(2)( :' (V)/(t)=av)`
`(L^(2))sqrt(2g(y))=piR^(2)sqrt(2g(4y))impliesR=(L)/(sqrt(2pi))`