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Q.

A solid sphere of radius R, made up of a 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. When a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere is

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a

MgAK

b

Mg3AK

c

3MgAK

d

Mg2AK

answer is B.

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Detailed Solution

Change in pressure due to placing of mass on piston is Δp=MgAFrom bulk modulus definition K=−dpdV/V           dVV=ΔpK=MgAKFrom  V=43πr3dVV=3dRR⇒dRR=13dVV=Mg3AK
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A solid sphere of radius R, made up of a 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. When a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere is