**Question:**

**A uniform cylinder of length $\mathrm{L}$ and mass $\mathrm{M}$ having crosssectional 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 :**

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

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

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

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

Question of from chapter.

JEE Main Previous Year April 25, 2013

Correct Option: 1

**Solution:**

(1)

### Related Questions

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\begin{aligned}

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## A uniform cylinder of length $\mathrm{L}$ and mass $\mathrm{M}$ having crosssectional 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. The extension $\mathrm{x}_{0}$ of the spring when it is in equilibrium is:

Question:A uniform cylinder of length $\mathrm{L}$ and mass $\mathrm{M}$ having crosssectional 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. The extension $\mathrm{x}_{0}$ of the spring when it is in equilibrium is:$\frac{\mathrm{Mg}}{\mathrm{k}}$

$\frac{\mathrm{Mg}}{\mathrm{k}}\left(1-\frac{\mathrm{LA} \sigma}{\mathrm{M}}\right)$

$\frac{\mathrm{Mg}}{\mathrm{k}}\left(1-\frac{\mathrm{LA\sigma}}{2 \mathrm{M}}\right)$

$\frac{\mathrm{Mg}}{\mathrm{k}}\left(1+\frac{\mathrm{LA} \sigma}{\mathrm{M}}\right)$

JEE Main Previous Year Single Correct Question of JEE Main from Physics Mechanical Properties of Fluids chapter.

JEE Main Previous Year 2013

Correct Option: 3

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