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`.

A solid sphere of radius `R` made of a material of bulk modulus `B` is

1.	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» Correct Answer - C Increase in pressure is `Deltap = (Mg)/A` Bulk modulus is ` B =Delta_(p)/((DeltaV//V))` `:.(DeltaV)/V = (Delta_(p))/B =( Mg)/(AB)` ….(i) Also, the volume of the sphere is `V = 4/3 piR^(3) rArr (Delta V)/V = (3 Delta R)/R` or `(Delta R)/R = 1/3. (DeltaV)/R`, Using Eq.(i) , we get ` (DeltaR)/R =( Mg)/(3 AB) rArr :. alpha = 3`

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