Tanks A and B open at the top contain two different liquids upto certain height in them. A hole is made to the wall of each tank at a depth h from the surface of the liquid. The area of the hole in B is twice that of in A. If the liquid mass flux through each hole is equal, then the ratio of the densities of the liquids respectively, is

Options

A. 1
B. `3/2`
C. `2/3`
D. `1/2`

Answer

A

Explanation

Using continuity equation
`therefore V_(2) =V_(1)/2` [ `because A_(2) = 2A_(1)`]
Mass of the liquid coming out of hole A is `m_(1)` anf from B is `m_(2)`.
`m_(1) = A_(1)V_(1) rho_(1)`
`m_(2) = A_(2)V_(2)rho_(2) = 2A_(1) V_(1)/2 rho_(2) = A_(1)V_(1)rho_(2)`
But, `A_(1)V_(1)rho_(1) = A_(2)V_(2)rho_(2)` [`because m_(1) = m_(2)`]
`rho_(1)/rho_(2) =1`