A wooden cylinder of length L is partly submerged in a liquid of specific gravity `rho_(1)` with `n^(th)` `(nlt1)` part of it inside the liquid. Another immiscible liquid of density `rho_(2)` is poured to completely submerge the cylinder. Density of cylinder `rho` is the geometric mean of the densities of the two liquid.
Similarly as above, find the time period of small oscillations above the mean position.

Options

A. `pi[(nL)/(g)]^((1)/(2))`
B. `pi[(L)/(ng)]^((1)/(2))`
C. `pi[((n-1)L)/(g)]^((1)/(2))`
D. `pi[(nL)/((n-1)g)]^((1)/(2))`

Answer

A

Explanation

Restoring force `=-Axrho_(1)g`
`Alrhoa=-Ax(rho)/(n).g,(x)/(a)=-(nL)/(g)`
`(T_(2))/(2)=pisqrt(|(x)/(a)|)=pi[(nL)/(g)]^((1)/(2))`