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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 equilibrium is:

A

`(Mg)/(k)`

B

`(Mg)/(k)(1 - (LAsigma)/(M))`

C

`(Mg)/(k)(1 - (LAsigma)/(2M))`

D

`(Mg)/(k)(1 + (LAsigma)/(M))`

Text Solution

Verified by Experts

The correct Answer is:
C
`kx_(0) + F_(B) = mg`
`kx_(0) + sigma(L)/(2)Ag = Mg`
`x_(0) = (Mg - (sigmaLAg)/(2))/(k)`
`= (Mg)/(k)(1 - (sigmaLA)/(2M))`
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