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

Answer

B

Explanation

Square hole, area `a_1 = L^2, v_1 = sqrt(2 gy)`
Circular hole, area `a_2 = pi R^2, v_2 = sqrt(2 g. 4y)`
`L^2. sqrt(2 gy) = pi R^2 sqrt(2 g. 4y)`
`L^2 = 2 pi R^2`
`R = (L)/(sqrt(2) pi)`.