In the figure shown, the heavy cylinder (radius R) reasting on a smooth surface separates two liquids of densities `2rho` and `3rho`. The height h for the equilibrium of cylinder must be

Options

A. `3R//2`
B. `Rsqrt((3)/(2))`
C. `Rsqrt(2)`
D. None of these

Answer

B

Explanation

Torque of hydrostatic force about centre of sphere is already zero as hydrostatic force passes through the centre.
`:. F_(LHS) = F_(RHS)`
`:. (1)/(2) (2rho) (g) h^(2) = (1)/(2) (3 rho) (g) R^(2)`
`:. h sqrt((3)/(2))R`