Bulk Modulus

The bulk modulus measures a material's resistance to uniform compression and is defined as $B=-\frac{\Delta P}{\Delta V/V}$, where the negative sign reflects that increased pressure reduces volume. Taking magnitudes, the fractional volume change is $\left|\frac{\Delta V}{V}\right|=\frac{\Delta P}{B}$, so a stiffer material compresses less for the same pressure rise. Inserting the excess pressure $\Delta P=2\times 10^7\text{Pa}$ and $B=1\times 10^{11}\text{Pa}$ gives $\frac{\Delta V}{V}=\frac{2\times 10^7}{1\times 10^{11}}=2\times 10^{-4}$. The value $5\times 10^{-4}$ would require a smaller bulk modulus. The value $2\times 10^{-3}$ misplaces a power of ten. The value $5\times 10^{-3}$ both inverts the ratio and shifts an exponent. This is exactly how NCERT relates hydrostatic pressure to volumetric strain for solids and liquids, where uniform pressure acts equally on every face and changes only the volume, not the shape. The reciprocal of the bulk modulus is the compressibility, so the very large value of $B$ for solids is equivalent to saying they are nearly incompressible. Note also that the excess pressure quoted is the gauge pressure due to the water column alone, since the atmospheric contribution acts on the surface sample too and is already accounted for. As a check, an extremely small fractional change is expected because solids have very large bulk moduli, so the sphere should barely shrink under deep-sea pressure.