A jar is filled with two non-mixing liquids 1 and 2 haivng densities `rho_1` and `rho_2` respectively. A solid ball, made of a material of density `rho_3` , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for `rho_1`, `rho_1` and `rho_3`?

Options

A. `rho_1 gt rho_3 gt rho_2`
B. `rho_1 gt rho_2 gt rho_3`
C. `rho_1 lt rho_3 lt rho_2`
D. `rho_1 lt rho_1 lt rho_2`

Answer

C

Explanation

`W = F_B`
`rho_3 Vg = rho_1 (V)/(2) g + rho_2 (V)/(2) g`
`rho_3 = (rho_1+ rho_2)/(2), rho_3` lies between `rho_1` and `rho_2`
`rho_2 gt rho_1`
`rho_1 lt rho_3 lt rho_2`.