# 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 :

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 :

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

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

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

4. $2 \pi\left[\frac{M}{(k+A \sigma g)}\right]^{1 / 2}$

JEE Main Previous Year Single Correct Question of JEE Main from Physics Oscillations chapter.

JEE Main Previous Year April 25, 2013

Correct Option: 1

Solution:

(1)

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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:

1. $\frac{\mathrm{Mg}}{\mathrm{k}}$

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

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

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

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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