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 :

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)`