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  • A uniform cylinder of length L and mass M having cross-sectional are 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

A uniform cylinder of length L and mass M having cross-sectional are 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 T of the oscillation of the cylinder will be : 

Option: 1

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


Option: 2

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


Option: 3

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

 


Option: 4

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


Answers (1)

best_answer

 

 

 

If (x) is the displacement then,

\begin{array}{l} \therefore M \omega^{2} x=[ \sigma A g+k] x \\ \Rightarrow \omega=\left[\frac{ \sigma A g+k}{M}\right]^{1 / 2} \Rightarrow T= 2\pi \left[\frac{M}{\sigma A g+k}\right]^{1 / 2} \end{array}

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