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

Answer

D

Explanation

The object is spherical and the bulk modulus is represented by B. It is the ratio of normal stress to the volumetric strain.
Hence `B = (F//A)/(Delta V//V) rArr (Delta V)/(V) = (p)/(B) rArr |(Delta V)/(V)| = (p)/(B)`
Here p is applied pressure on the object and `(Delta V)/(V)` is volume strain
Fractional decreases in volume
`rArr (Delta V)/(V) = 3(Delta R)/(R) " " [because V = (4)/(3)pi R^(3)]`
Volume of the sphere decreases due to the decreases in its radius.
Hence `(Delta V)/(V) = (3Delta R)/(R) = (p)/(R) rArr (Delta R)/(R) = (p)/(3B)`