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)
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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
Solution:
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