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.
Calculate the fraction of the cylinder submerged in the lower liquid after the upper liquid is poured in the vessel

Options

A. `(n)/((n+1))`
B. `((n-1))/((n+1))`
C. `(n(n-1))/((n+1))`
D. `(n(n-1))/((n+1))`

Answer

A

Explanation

`rhoth` part `(plt1)` is in lower liquid up thrust `=` weight `Ap((rho)/(n))+A(1-p)rho.n=Arho`
or `((rho)/(n))+n-pn=1,p=(n(1-n))/((1-n^(2)))=(n)/((n+1))`