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A uniform cylinder of length L and mass ...

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 `sigma` at equilibrium position. The extension `x_0` of the spring when it is in equlibrium is:

A

`(Mg)/(k)`

B

`(Mg)/(k) (1 - (LA sigma)/(M))`

C

`(Mg)/(k) (1 - (LA sigma)/(2M))`

D

`(Mg)/(k) (1 + (LA sigma)/(M))`

Text Solution

Verified by Experts

The correct Answer is:
C
At equilibrium ` sum F_("net") = 0 `
`k x _(0) + F_(B) = Mg`
`rArr k x _(0) = sigma ((L)/(2)) Ag = Mg `
`rArr kx_(0) + Mg - sigma (L)/(2) Ag`
`x_(0) = (Mg)/(k) (1 - (L A sigma)/(2 M))`
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