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

Options

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

Answer

A

Explanation

Equating the rate of flow, we have, `A_(1)v_(1)=A_(2)v_(2)`
`rArrsqrt((2gY))xxL^(2)=sqrt((2gxx4Y))piR^(2)" "rArr" "L^(2)=2piR^(2)rArrR=(L)/(sqrt(2pi))`