A uniform cylinder of length L and mass M having crosssectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density `sigma` at equilibrium position. The extension `x_(0)` of the spring when it is in equilibrium is :

Options

A. `(Mg)/k(1-(Lasigma)/M)`
B. `(Mg)/k(1-(LAsigma)/(2M))`
C. `(Mg)/k(1+(LAsigma)/M)`
D. `(Mg)/k`

Answer

B

Explanation

At equilibrium `sumF = 0`
`kx_(0)+((AL)/2sigmag)-Mg=0`
`x_(0)=Mg[1-(Lasigma)/(2M)]`
So, correct choice is (b).