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 :

Explanation

`k=(-/_\p)/(/_\V//V)`, where `/_\p=(Mg)/A`
`:. (-/_\V)/V-(Mg)/(Al)`
`implies -((V_(i)-V_(f)))/(V_(i)-(Mg)/(Ak)`
`implies (4/3piR^(3)-4/3pi(R-deltaR)^(3))/(4/3piR^(3))=(Mg)/(Ak)`
`implies(R^(3)-[R^(3)-3R^(2)deltaR])/(R^(3)) =(Mg)/(Ak)`
`(deltaR)/R=(Mg)/(3Ak)`