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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
  • ASmaller than $2\pi {\left[ {\frac{M}{{\left( {k + A\sigma g} \right)}}} \right]^{1/2}}$
  • B$2\pi \sqrt {\frac{M}{k}} $
  • CLarger than $2\pi {\left[ {\frac{M}{{\left( {k + A\sigma g} \right)}}} \right]^{1/2}}$
  • D$2\pi {\left[ {\frac{M}{{\left( {k + A\sigma g} \right)}}} \right]^{1/2}}$
JEE MAIN 2013, Diffcult
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