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

`((Mg)/(3AK))`

Explanation

`((Mg)/(3AK))`
`Deltap=(Mg)/(A)rArr|(DeltaV)/(V)|=(Deltap)/(k)=(Mg)/(AK),"Now"V=(4)/(3)piR^(3)orVpropR^(3)`
`therefore(DeltaV)/(V)=3((DeltaR)/(R))or(DeltaR)/(R)=(1)/(3)((DeltaV)/(V))`... (i)
`therefore"From equation"(i)(DeltaR)/(R)=(Mg)/(3AK)`