A solid sphere of radius r made of a soft 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, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere, `((dr)/(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)`