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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 σ 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 :

Smaller than 2 π [(M)/((k+A σ g)) ]^1 / 2

Larger than 2 π [(M)/((k+A σ g)) ]^1 / 2

Oscillations

JEE Main level, single correct, medium

179 of 194

Question 179 of 194

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 :

Show answer and solution

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

No solution is given.

JEE Main question paper PDF

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JEE Main 2025 Apr 2 Shift 1 question paper

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JEE Main Physics practice question on Oscillations (Applications of SHM), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.