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

Explanation

According to Bernoulli's theorem
For `v_(1),P+rhog((h)/(2))=P+(1)/(2)(rho)(v_(1)^(2))impliesv_(1)=sqrt(gh)`
For `v_(2),P+(rhogh)+(2rho)g((h)/(2))=P+(1)/(2)(2rho)v_(2)^(2)`
`impliesv_(2)=sqrt(2gh)`
`:. (v_(1))/(v_(2))=(1)/(sqrt(2))`