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)/(kA)`
B. `(Mg)/(3kA)`
C. `(Mg)/(2kA)`
D. `(Mg)/(4kA)`

Answer

B

Explanation

`k=v(dp)/(dv)`
`therefore (dv)/(v)=(dp)/(k) " " ` …(i)
`V prop r^(3)`
`therefore (dv)/(v) =(3dr)/(r ) " " ` …(ii)
From equation (i) and (ii),
`(dp)/(k)=(3dr)/(r )=(1)/(3)(dp)/(k)=(F)/(3Ak)=(mg)/(3Ak)`