A solid sphere of radius ‘R’ made of a material of bulk modulus B is surrounded by a liquid in a cylindrical container. A massless piston of area ‘A’ floats on the surface of the liquid. Find the fractional change in the radius of the sphere (dRR) , when a mass M is placed on the piston to compress the liquid.

Question

A solid sphere of radius ‘R’ made of a material of bulk  modulus B is surrounded by a liquid in a cylindrical container. A massless  piston of area ‘A’ floats on the surface of the liquid. Find the fractional  change in the radius of the sphere (dRR)     , when a mass M is placed on the piston to compress the  liquid.

Infinity Learn · Accepted Answer

As fro a spherical body $$V=43$$$$π$$$$R3$$,Δ$$VV=3$$ΔRR       Now by definition of bulk $$modulusB=$$−VΔPΔVi.e|ΔVV|$$=$$Δ$$PB=MgAB$$[as  Δ$$P=MgA$$]     $$dRR=13$$ΔVV⇒$$dRR=Mg3AB$$

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