QJEEM13Ph3318: JEE Main 2013 Physics - Class 11 JEEM13Ph3318 Solution: A uniform cylinder of length L and mass M having…

Question

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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 mass-less spring such that it is half submerged in a liquid of density

σ

at equilibrium position. The extension

x_{0}

of the spring when it is in equilibrium is:

Accepted Answer

From figure,

k x_{0} + F_{B} = M g

k x_{0} + σ \frac{L}{2} A g = M g

[ as mass

=

density

\times

volume ]

\Rightarrow k x_{0} = M g - σ \frac{L}{2} A g

\Rightarrow x_{0} = \frac{M g - \frac{σ L A g}{2}}{k}

= \frac{M g}{k} (1 - \frac{L A σ}{2 M})

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