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. Ba/mg
B. Ba/3mg
C. mg/3Ba
D. mg/Ba

Answer

c

Explanation

In volume of shpere in liquid.
When mass m is placed on the piston, the increased pressure `P = (mg)/(a)`. Since, this increased pressue is
equally applicable to all directions on the sphere, so there will be decreases in volume of sphere, due to decrease in its radius. From Eq. (i) change in volume is
`Delta V = (4)/(3) pi xx 3 r^(2) Delta r = 4 pi r^(2) Delta r`
`:. (Delta V)/(V) = (4 pi r^(2) Delta r)/((4//3) pi r^(3)) (3 Delta r)/(r )`
Now, `B = (P)/(dV//V) (mg)/(a) xx (r )/(3 Delta r)`
`:. (Delta r)/(r ) = (mg)/(3Ba)`