Question

A vertical pole of length `l`, density `rho`, area of cross section `A`, floats in two immiscible liquids of densities `rho_(1)` and `rho_(2)`. In equilibrium position the bottom end is at the interface of the liquids. When the cylinder is displaced vertically, the time period of oscillation is..........

A. `pisqrt((rhol)/((rho_(1)+rho_(2))g))`
B. `pi sqrt((rhol)/(g)) ((1)/(sqrt(rho_(1)))+(1)/(sqrt(rho_(2))))`
C. `pi sqrt(((rho_(1)+rho_(2))l)/(rhog))`
D. `pi sqrt((l)/(rhog)) (sqrt(rho_(1))+sqrt(rho_(2)))`

Answer 1

Correct Answer - B
Here interface acts as mean position of `SHM`:
`:.` time period, `T = (T_(1))/(2) +(T_(2))/(2)`
`T_(1) = 2pi sqrt((rhol)/(rho_(2)g)): T_(2) = 2pi sqrt((rhol)/(rho_(1)g))`