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

Answer

`Rsqrt((3)/(2))`

Explanation

For equilibrium of cylinder `F_(x)` should be balanced
`P_(3rho)xxRL = P_(2rho) xx hL`
`(R(3rho)g)/(2)xxRL=(h(2rho)g)/(2)xxhL`
`3R^(2)=2h^(2)`
`h = sqrt((3)/(2))R`