A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylinderical container. A massless piston of area a floats on the surface of the liquid, convering 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

A solid sphere of radius r made of a soft material of bulk modulus K i

1.	A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylinderical container. A massless piston of area a floats on the surface of the liquid, convering 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
Answer» `(mg)/(3Ka)` `(mg)/(Ka)` `(Ka)/(mg)` `(Ka)/(3mg)` Solution :BULK modulus , `K=-V(dp)/(DV)` or, `(dV)/V=(dP)/K` or,`(-3dr)/r=((mg)/a)/K[becauseV/3pir^3]` or,`(DR)/r=-(mg)/(3Ka) therefore \|(dr)/r\|=(mg)/(3Ka)`