Equal volume of two immissible liquid of densities `rho` and `2 rho` are filled in a vessel as shown in Fig. 7(CF).15. Two small holes are punched at depth `(h)/(2)` and `(3h)/(2)` from the surface of lighter liquid. If `v_(1)` and `v_(2)` are the velocities of efflux at these two holes, then `v_(1)//v_(2)` is

Options

A. `(1)/(4)`
B. `(1)/(2)`
C. `(1)/(sqrt(2))`
D. `(1)/(2sqrt(2))`

Answer

C

Explanation

`v_(1) =sqrt(2 gh(h//2)) =sqrt(gh)` ….(i)
Using Bernoulli's Theorem
`rho gh+2 rho g ((h)/(2))=(1)/(2) (2 rho) v_(2)^(2)` or `v_(2) =sqrt(2 gh)`
`:. (v_(1))/(v_(2)) =(1)/(sqrt(2))`