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A large open tank has two holes in its w...

A large open tank has two holes in its wall. One is a square hole of side a at a depth of x from the top and the other is a circular hole of radius r at a depth 4x 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

A

`2 pi a`

B

a

C

`(a)/(2pi)`

D

`(a)/(sqrt(2 pi))`

Text Solution

Verified by Experts

The correct Answer is:
D
We have `v^(2) = rho gh`
`a^(2) sqrt(rho gh) = pi r^(2) sqrt(rho gh) xx 2`
`r = (a)/(sqrt(2 pi))`
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