To solve this problem, we need to understand the relationship between bulk modulus, pressure, and the change in volume.$\\$The bulk modulus $B$ is defined as:$\\ B = -\frac{\Delta P}{\frac{\Delta V}{V}} \\$where $\Delta P$ is the change in pressure, $\Delta V$ is the change in volume, and $V$ is the original volume.$\\$For a spherical object, the volume $V$ is given by:$\\ V = \frac{4}{3} \pi r^3 \\$where $r$ is the radius of the sphere.$\\$The change in volume $\Delta V$ due to a small change in radius $\Delta r$ is:$\\ \Delta V = \frac{d}{dr}\left(\frac{4}{3} \pi r^3\right) \cdot \Delta r = 4 \pi r^2 \cdot \Delta r \\$The fractional change in volume is:$\\ \frac{\Delta V}{V} = \frac{4 \pi r^2 \cdot \Delta r}{\frac{4}{3} \pi r^3} = \frac{3 \Delta r}{r} \\$Substituting this into the bulk modulus equation:$\\ B = -\frac{\Delta P}{\frac{3 \Delta r}{r}} \\$Rearranging to solve for the fractional change in radius:$\\ \frac{\Delta r}{r} = -\frac{\Delta P}{3B} \\$Since the pressure $P$ is applied uniformly, we have $\Delta P = P. \\$Thus, the fractional decrease in radius is:$\\ \frac{\Delta r}{r} = \frac{P}{3B} \\$This corresponds to Option 3.