A large open tank has two holes in the wall. The top hole is a square hole of side L at a depth y from the surface of water. The bottom hole is a circular hole of radius R at a depth 4y from surface of water . If `R=L//2 sqrt(pi)`, find the correct graph. `V_(1)` and `V_(2)` are the velocities in top and bottom holes. Area of the square & curcular holes are `a_(1)` and `a_(2)`

Options

A.
B.
C.
D.

Answer

B

Explanation

`R=L//2sqrt(pi)`
`4piR^(2)=L^(2)` or `4piR^(2)sqrt(2gy)=L^(2)sqrt(2gy)`
or `2a_(2)V_(2)=a_(1)V_(1)` where `a_(1)=L^(2), a_(2)=piR^(2)`
`V_(1)=sqrt(2gy),V_(2)=sqrt((2g(4y))/`, so `((a_(1))/(a_(2)))=((2V_(2))/(V_(1)))`