Question

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 .............

Answer 1

`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)`