A solid uniform ball of volume `V` floats on the interface of two immiscible liquids (see the figure). The specific gravity of the upper liquid is `rho_(1)` and that of lower one is `rho_(2)` and the specific gravity of ball is `rho(rho_(1)gtrhogtrho_(2))` The fraction of the volume the ball in the upper liquid is

Options

A. (a) `(rho_2)/(rho _1 ) `
B. (b)` (rho_2- rho ) /(rho_2 - rho_1 ) `
C. (c)`(rho - rho _1 )/(rho _ 2 - rho _1 ) `
D. (d)` (rho _1 )/(rho_2 ) `

Answer

B

Explanation

`Vrhog=vrho_(1)g+(V-v)rho_(2)g" "Rightarrow" "V(rho-rho_(2))=v(rho_(1)-rho_(2))" "Rightarrow" "(v)/(V)=(rho-rho_(2))/(rho_(1)-rho_(2))`