A uniform cylinder of length and mass having cross-sectional area is suspended

PHYSICS · Single correct · CBSE · Physics · Oscillations · Oscillations

Problem

A uniform cylinder of length LL and mass MM having cross-sectional area AA 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 σ\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 TT of the oscillations of the cylinder will be : [Main Online April 25, 2013] (1) Smaller than 2π[M(k+Aσg)]1/22\pi \left[ \frac{M}{(k + A\sigma g)} \right]^{1/2} (2) 2πMk2\pi \sqrt{\frac{M}{k}} (3) Larger than 2π[M(k+Aσg)]1/22\pi \left[ \frac{M}{(k + A\sigma g)} \right]^{1/2} (4) 2π[M(k+Aσg)]1/22\pi \left[ \frac{M}{(k + A\sigma g)} \right]^{1/2}

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