Equal volume of two immiscible liquids of densities `rho` and `2rho` are filled in a vessel as shown in the figure. Two small holes are punched at depths `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)/(2sqrt(2))`
B. `(1)/(2)`
C. `(1)/(4)`
D. `(1)/(sqrt(2))`

Answer

D

Explanation

`P_(0)+rhog.(h)/(2)=P_(0)+(1)/(2)rhov_(1)^(2)`
`P_(0)+rhog.(h)/(2)+(2rho)g.(h)/(2)=P_(0)+(1)/(2)(2rho)v_(2)^(2)`
`(v_(1))/(v_(2))=(sqrt(gh))/(sqrt(2gh))=(1)/(sqrt(2))`