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 .............

Options

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

Answer

B

Explanation

Change in pressure due to placing of mass of prism is `/_\p=(Mg)/A`
From bulk modulus definition `K=(-dp)/(dV//V)`
`|(dV)/V|=(/_\P)/K=(Mg)/(AK)`
From `V=4/3pir^(3)`
`(dV)/V=(3dR)/Rimplies(dR)/R=1/3(dV)/V=(Mg)/(3AK)`