A solid sphere of radius R made of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless pistion 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, `deltaR//R`, is .............

Options

A. `(mg)/(AK)`
B. `(mg)/(3AK)`
C. `(mg)/(A)`
D. `(3mg)/(AK)`

Answer

B

Explanation

`(DeltaV)/(V) = (F)/(AK) = (mg)/(AK), (Delta R)/(R) = (1)/(3) (Delta V)/(V)`