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 in a liquid of density $\sigma$ at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period T of the oscillations of the cylinder will be: (1) Smaller than $2\pi \left[ \frac { M } { ( k + A\sigma g ) } \right] ^ { 1/2 }$ (2) $2\pi \sqrt { \frac { M } { k } }$ (3) Larger than $2\pi \left[ \frac { M } { ( k + A\sigma g ) } \right] ^ { 1/2 }$ (4) $2\pi \left[ \frac { M } { ( k + A\sigma g ) } \right] ^ { 1/2 }$
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 in a liquid of density $\sigma$ at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period T of the oscillations of the cylinder will be:\\
(1) Smaller than $2\pi \left[ \frac { M } { ( k + A\sigma g ) } \right] ^ { 1/2 }$\\
(2) $2\pi \sqrt { \frac { M } { k } }$\\
(3) Larger than $2\pi \left[ \frac { M } { ( k + A\sigma g ) } \right] ^ { 1/2 }$\\
(4) $2\pi \left[ \frac { M } { ( k + A\sigma g ) } \right] ^ { 1/2 }$