Equal volume of two immiscible liquids of densities `rho and 2 rho` are filled in a vessel as shown in figure. Two small holes are punched at depths `(h)/(2) and (3h)/(2)` from the surface of lighter liquid. If `v_(1) and v_(20` are the velocities of efflux at these two holes, then `(v_(1))/(v_(2))` is

Options

A. `(1)/(2 sqrt2)`
B. `(1)/(2)`
C. `(1)/(4)`
D. `(1)/(sqrt2)`

Answer

D

Explanation

`v_(1) = sqrt(2g ((h)/(2))) = sqrtgh`
Using Bernoulli.s theorem, we get
`P_(a) + rho gh + 2 rh g ((h)/(2)) = P_(a) + (1)/(2) (2rho) v_(2)^(2) or v_(2) = sqrt(2 gh)`
`:. (v_(1))/(v_(2)) = (1)/(sqrt2)`