$A$ 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

• A
  Smaller than $2\pi \left[ \frac{M}{k + A\sigma g} \right]^{1/2}$
• B
  $2\pi \sqrt{\frac{M}{k}}$
• C
  Larger than $2\pi \left[ \frac{M}{k + A\sigma g} \right]^{1/2}$
• D
  $2\pi \left[ \frac{M}{k + A\sigma g} \right]^{1/2}$