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Uniform cylinder having length L and mass M having cross sectional area A is hung vertically downward from a stationary point by a massless spring, such that it is half submerged in a given liquid of density σ at mean position. Then find the extension x0 in the spring when it is in mean position:

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a

Mgk1−LAσ2M

b

Mgk1+LAσM

c

Mgk

d

Mgk1−LAσM

answer is A.

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Detailed Solution

kx0+FB=mgkx0+σL2Ag=Mgx0=Mg−σω02k=Mgk1−σ⌞A2M

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Uniform cylinder having length L and mass M having cross sectional area A is hung vertically downward from a stationary point by a massless spring, such that it is half submerged in a given liquid of density σ at mean position. Then find the extension x0 in the spring when it is in mean position: