# 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 flo

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

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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)