question_answer

                A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, form a fixed point by a mass less  spring, such that it is half submerged in a liquid of density \[\sigma \]at equilibrium position. When the cylinder is given a downward push and released, it stats oscillating vertically with a small amplitude. The time period T of the oscillations of the cylinder will be:     JEE Main Online Paper ( Held On 25  April 2013 )

A)                 Smaller than \[2\pi \]\[{{\left[ \frac{\operatorname{M}}{\operatorname{k}+\operatorname{A}\sigma g} \right]}^{1/2}}\]

B)                                        \[2\pi \sqrt{\frac{\operatorname{M}}{\operatorname{k}}}\]

C)                                        Larger than \[2\pi {{\left[ \frac{\operatorname{M}}{(\operatorname{k}+\operatorname{A}\sigma g)} \right]}^{1/2}}\]

D)                                        \[2\pi {{\left[ \frac{\operatorname{M}}{(\operatorname{k}+\operatorname{A}\sigma g)} \right]}^{1/2}}\]