A uniform cylinder of length L and mass M having cross-sectional...

A uniform cylinder of length

\mathrm{L}

and mass

M

having cross-sectional area

\mathrm{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

\mathrm{T}

of the oscillations of the cylinder will be :

Options

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

Correct answer

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

Step-by-step solution

No solution is given.

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