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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

(a) `(Mg)/(k)`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
From figure, `kx_0+F_B=Mg`
`kx_0+sigmaL/2Ag=Mg`
[ `:'` mass density xx volume]
`implieskx_0=Mg-sigmaL/2Ag`
`impliesx_0=(Mg-(sigmaLAg)/(2))/(k)=(Mg)/(k)(1-(LAsigma)/(2M))`
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