1)

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, (drr) is


A) Kamg

B) Ka3mg

C) mg3Ka

D) mgKa

Answer:

Option C

Explanation:

   Bulk modulus.

 K= VolumetricstressVolumetricstrain=pvv

K=mga(3rr)[V=43πr3,soVV=3rr]

             rr=mg3aK