The bulk modulus of a spherical object is `B` if it is subjected to uniform pressure `p`, the fractional decrease in radius is:

Options

A. `(B)/(3p)`
B. `(3p)/(B)`
C. `(p)/(3B)`
D. `(p)/(B)`

Answer

C

Explanation

Bulk modulus B is given as `B= (-pV)/(Delta V)` …(i)
The volume of a spherical object of radius r is given as `V= (4)/(3) pir^(3), Delta V= (4)/(3) pi (3r^(2)) Delta r :. (V)/(Delta V) = (r )/(3 Delta r)`
Put this value in eqn (i), we get `B= (pr)/(3 Delta r)`
Fractional decrease in radius is, `(Delta r)/(r ) = (p)/(3B)`