Q.A solid sphere of volume $1000\ \text{cm}^3$ is lowered into a fluid where it experiences a uniform increase in pressure of $2.0\times10^{7}\ \text{Pa}$ on its entire surface. If the bulk modulus of the material of the sphere is $K = 1.6\times10^{11}\ \text{Pa}$, find

Given: $V = 1000\ \text{cm}^3 = 1.0\times10^{-3}\ \text{m}^3$, $\Delta P = 2.0\times10^7\ \text{Pa}$, $K = 1.6\times10^{11}\ \text{Pa}$.

1. Fractional decrease in volume, from $K = -\Delta P/(\Delta V/V)$, i.e. $|\Delta V/V| = \Delta P/K$:

   $\frac{\Delta V}{V} = \frac{\Delta P}{K} = \frac{2.0\times10^7}{1.6\times10^{11}} = 1.25\times10^{-4}$

2. Actual decrease in volume: $\Delta V = 1.25\times10^{-4} \times V = 1.25\times10^{-4} \times 1.0\times10^{-3}\ \text{m}^3 = 1.25\times10^{-7}\ \text{m}^3$ …

Rearrange $K = -\Delta P/(\Delta V/V)$ to $\Delta V/V = \Delta P/K$ (the minus sign only fixes the sign convention, so magnitudes are used directl …

• Forgetting to convert $\text{cm}^3$ to $\text{m}^3$ (or back) consistently, since $K$ and $\Delta P$ are in SI (Pa) units. …