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 :

Options

A. `(Mg)/(AK)`
B. `(Mg)/(2AK)`
C. `(Mg)/(3AK)`
D. `(Mg)/(4AK)`

Answer

C

Explanation

`DeltaP=(Mg)/A`
`|(DeltaV)/V|=(DeltaP)/K=(Mg)/(AK)`
Now, as `V=4/3 pi R^(3)` or `V prop R^(3)`
`:. (DeltaV)/V=3((DeltaR)/R)`
or `(DeltaR)/R=1/3 ((DeltaV)/V)......(1)`
`:.` from equation (1)
`(DeltaR)/R=(Mg)/(3AK)`