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.....

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 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.....
Answer» `(Ka)/(mg)` `(Ka)/(3MG)` `(mg)/(3Ka)` `(mg)/(Ka)` Solution :Bulk modulus `= ("VOLUME stress")/("volume strain")` `= (("Force")/("Area "))/( ( "change in volume")/("volume"))` `therefore (Delta V )/( V) = (mg )/(ka)` but, vlume of sphere `V = 4/3 PI R ^(3),` `therefore (Delta V )/(V) =3 (Delta r )/(r)` `therefore (Delta r )/( r ) = 1/3 xx (Delta V )/(V) = (mg )/(3Ka )`