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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…

JEE Main 2013 — Physics Waves & Oscillations

2013mcqmedium

A uniform cylinder of length L\mathrm{L}L and mass MMM having cross-sectional area A\mathrm{A}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 σ\sigmaσ 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\mathrm{T}T of the oscillations of the cylinder will be :

Official previous-year question

Held on 25 Apr 2013 · Verified 6 Jul 2026.

Options

  1. A

    Smaller than 2π[M(k+Aσg)]1/22 \pi\left[\frac{M}{(k+A \sigma g)}\right]^{1 / 2}2π[(k+Aσg)M​]1/2

  2. B

    2πMk2 \pi \sqrt{\frac{M}{k}}2πkM​​

  3. C

    Larger than 2π[M(k+Aσg)]1/22 \pi\left[\frac{M}{(k+A \sigma g)}\right]^{1 / 2}2π[(k+Aσg)M​]1/2

  4. D

    2π[M(k+Aσg)]1/22 \pi\left[\frac{M}{(k+A \sigma g)}\right]^{1 / 2}2π[(k+Aσg)M​]1/2

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