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)/(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)`