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 `((dR)/(R ))`, when a mass M is placed on the piston to compress the liquid.

Explanation

As for a spherical body
`V=(4)/(3) pi R^(3), (DeltaV)/(V) =3(DeltaR)/(R )`
Now by definition of bulk modulus
`B= -V(DeltaP)/(DeltaV)i.e |(DetlaV)/(V)| =(DeltaP)/(B) rArr (Mg)/(AB) ["as "DeltaP=(Mg)/(A)]`
`(dR)/(R )=(1)/(3)(DeltaV)/(V) rArr (dR)/(R )=(Mg)/(3AB)`