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

Applying Bernoulli's theorm at open surface and at first holes.
`P+0+(h)/(2)rhog=P+(1)/(2)rhov_(1)^(2)+0implies" "v_(1)=sqrt(gh)" "....(1)`
Applying Bernoulli's theorem at interface of liquid and at second hole
`(P+hrhog)+0+(h)/(2).(2rho).g=P+(1)/(2)(2rho)v_(2)^(2)+0impliesv^(2)=sqrt(2gh)" "....(2)`
From (1) and (2)
`(v_(1))/(v_(2))=(1)/(sqrt(2))`