question_answer

A uniform cylinder of length L and mass M having cross - sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged n a liquid  of density \[\sigma \] at equilibrium position. The extension\[{{x}_{0}}\]of the spring when it is in equilibrium is:                                             [JEE MAIN 2013]

A)  \[\frac{Mg}{k}\]           

B)       \[\frac{Mg}{k}\left( 1-\frac{LA\sigma }{M} \right)\]

C)  \[\frac{Mg}{k}\left( 1-\frac{LA\sigma }{2M} \right)\]

D)       \[\frac{Mg}{k}\left( 1+\frac{LA\sigma }{M} \right)\] (Here, k is spring constant)

Correct Answer: C

Solution :

[c]