Physics

Problem

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 : [Main Online April 25, 2013] a. Smaller than

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

2\pi \sqrt{\frac{M}{k}}

c. Larger than

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

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

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