A solid sphere of radius `R` made of a material of bulk modulus `B` is surrounded by a liquid in a cylindrical container. A massless piston of area `A` (the area of container is also `A`) floats on the surface of the liquid. When a mass `M` is placed on the piston to compress the liquid , fractional change in radius of the sphere is `(Mg)/(alpha AB)`. Find the value of `alpha`.

Answer

9

Explanation

Increase in pressure is `Deltap=(Mg)/(A)`
Bulk modulus is `B=(DeltaP)/((DeltaV//V))`
`therefore(DeltaV)/(V)=(DeltaP)/(B)=(Mg)/(AB)` … (i)
Also, the volume of the sphere is
`V=(4)/(3)piR^(3)rArr(DeltaV)/(V)=(3DeltaR)/(R)or(DeltaR)/(R)=(1)/(3).(DeltaV)/(V)`, using eq . (i) we get
`(DeltaR)/(R)=(Mg)/(3AB)thereforen=9`