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. `2 piL`
C. `sqrt((2)/(pi)*L`
D. `(L)/(2pi)`

Answer

C

Explanation

Let `v_(1)` and `v_(2)` be the velocity of efflux from square and circular hole respectively. `S_(1) and S_(2)` be cross-section areas of square and circular holes.
`v_(1) = sqrt(8 gy) and v_(2) = sqrt(2g(y))`
The volume of water coming out of square and circular hole per second is
`Q_(1) =v_(1)S_(1) = sqrt(8gy) L^(2) , Q_(2) = v_(2)S_(2)`
`=sqrt(2gv) piR^(2) :' Q_(1) = Q_(2)`
`:. R = sqrt((2)/(pi))*L`.