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Question

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, drr , is :

Options

A.

Ka3 mg

B.

mg3 Ka

C.

mgKa

D.

Kamg

Solution

[Bulk Modulus = volumetric stressvolumetric strain]
K=mgadVV
dVV=mgKa    ...(i)
volume of sphere → V = 43πR3
Fractional change in volume dVV=3drr ...(ii)
U sing eq. (i) & (2) 3drr=mgKa
drr=mg3Ka

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