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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 (spring constant k) such that it is half submerged in a liquid of density σ at equilibrium position. The extension xo of the spring when it is in equilibrium is:

A
Mgk(1+LAσM)
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B
Mgk(1LAσ2M)
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C

Mgk

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D
Mgk(1LAσM)
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Solution

The correct option is B Mgk(1LAσ2M)
FBD of body in half submerged condition.


At equilibrium condition,
kx0+FB=Mg
kx0+σgV2=Mg
kx0+σg×AL2=Mg
kxo=(MgσgAL2)
xo=Mgk(1LAσ2M)
Tips: Draw the FBD of body and balance the forces in vertical direction.

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