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. `(P)/(B)`
B. `(P)/(3B)`
C. `(3P)/(B)`
D. `(B)/(3P)`

Answer

B

Explanation

Let R be the radius of the object. Then Volume of the object, `V= (4)/(3) pi R^(3) :. (Delta V)/(V) = 3 (Delta R)/(R )` …(i)
When it is subjecte dto uniform pressure P, the fractional decrease in volume is
`(Delta V)/(V) = (P)/(B)` …(ii)
From eqns. (i) and (ii), we get
`3(Delta R)/(R ) = (P)/(B) or (Delta R)/(R ) = (P)/(3B)`
`:.` Fractional decrease in radius is P/3B.