Solids: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Solids. Understanding the underlying formula is key to arriving at the correct answer below:

Bulk modulus $B = \frac{P}{\Delta V/V} \Rightarrow \frac{\Delta V}{V} = \frac{P}{B}$. For a sphere, $V = \frac{4}{3}\pi r^3$, so the fractional change in volume is $\frac{\Delta V}{V} = 3 \frac{\Delta r}{r}$. Therefore, $$\frac{\Delta r}{r} = \frac{1}{3} \frac{\Delta V}{V} = \frac{P}{3B}$$.