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 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, `deltaR//R`, is .............

Options

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

Answer

C

Explanation

`because` Bulk modulus , `K=("Volum etric stress")/("volumn etric stra in ")=(Deltap)/((DeltaV)/(V))`
`rArrK=(mg)/(a((3Deltar)/(r)))[becauseV=(4)/(3)pir^(3),"so"(DeltaV)/(V)=(3Deltar)/(r)]rArr(Deltar)/(r)=(mg)/(3ak)`