A solid sphere of radius R made of 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 δR/R is:-
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Question

A solid sphere of radius R made of 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 δR/R is:-

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G1 Physics · Accepted Answer

Use stress σ=F/A, strain ε=ΔL/L and Young's modulus Y=σ/ε. For a uniform segment, ΔL=FL/(AY); for thermal restraint, thermal strain αΔT produces stress YαΔT. Evaluating the given data/statements gives B: mg/3AK. Therefore the correct answer is B.