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

`v_(1)=sqrt(2g(h/2))=sqrt(gh)`…..i
From Bernoulli's theorem `rhog+2rhog(h/2)=1/2(2rho)v_(2)^(2)`
`impliesv_(2)=sqrt(2gh)`…….ii
`(v_(1))/(v_(2))=1/(sqrt(2))`