Question

The bulk modulus of a spherical objects is '$B$'. If it is subjected to uniform pressure '$P$', the fractional decrease in radius is:

• A. $\frac{P}{3B}$
• B. $\frac{P}{B}$
• C. $\frac{B}{3P}$
• D. $\frac{3P}{B}$

Answer 1

The correct option is A $\frac{P}{3B}$

Bulk modulus $B=-V\frac{△P}{△V}$
$B=\frac{-V\left(P\right)}{dV}{r}^3$
$B=\frac{-r^{3}P}{3r^{2}dr}$
$\frac{dr}{r}=\frac{P}{3B}$