A solid sphere of radius R and made of material of bulk modulus K is completely immersed in a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass 5M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere, 3:2 is given by

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M gK A

M g2K A

5M g3K A

M g4K A

answer is C.

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Detailed Solution

Pressure exerted by the piston on the liquid when a mass 5M is placed on the piston, P=5Mg/A . This pressure is exerted by the liquid equally in all directions. Therefore, the surface of the sphere experiences a force P per unit area. The stress on the sphere is P=5Mg/A . Now, the volume of the sphere isV=4πR33Due to stress, the change in the volume of the sphere isΔV=Δ(4πR33)=4π3.3R2ΔR=4πR2ΔR∴ volume strain ΔVV=3ΔRR By definition, bulk modulusK=stressstain=5Mg/A3ΔR/Ror ΔRR=5M g3K A

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