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Question

# A small solid sphere of radius R made of a material of bulk modulus B is surrounded by an incompressible liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. The magnitude of fractional change in the radius of the sphere (dRR)when a mass M is placed slowly on the piston to compress the liquid is:

A
Mg3AB
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B
MgAB
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C
3MgAB
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D
None of these
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Solution

## The correct option is A Mg3ABPressure formula,P=P0+ρghand P′=P0+ρgh+MgASo, ΔP=MgABulk modulus, B=ΔPΔV/Vor, ΔVV=ΔPBNow, V=43πr3So, lnV=ln43+lnπ+3lnRor, ΔVV=3ΔRRor, ΔRR=ΔV3V=ΔP3B=Mg3AB

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