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Question

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 massless spring such that it is half submerged in a liquid of density σ at
equilibrium position. The extension x0 of the spring when it is in equilibrium is :


A
Mgk(1+LAσM)
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B
Mgk
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C
Mgk(1LAσ2M)
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D
Mgk(1LAσM)
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Solution

The correct option is C Mgk(1LAσ2M)
Let k be the spring constant of spring and it gets extended by length x0 in the equilibrium position.

In equilibrium,


Using force balance along vertical direction,

kx0+FB=Mg

kx0+σL2Ag=Mg

x0=MgσLAg2k

x0=Mgk(1LAσ2M)

Hence, option (C) is correct.

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