Bulk Modulus And Compressibility

NCERT Class 11, Chapter 9 (Mechanical Properties of Solids) defines bulk modulus as the ratio of the applied normal pressure to the resulting fractional decrease in volume, $B=\frac{\Delta P}{(\Delta V/V)}$. This describes how strongly a material resists uniform compression on all sides. The volume change must be expressed in SI units: $\Delta V=100{\text{cm}}^3=100\times 10^{-6}{\text{m}}^3=1\times 10^{-4}{\text{m}}^3$. The volumetric strain is $\frac{\Delta V}{V}=\frac{1\times 10^{-4}}{0.5}=2\times 10^{-4}$. Therefore $B=\frac{2\times 10^7}{2\times 10^{-4}}=1\times 10^{11}\text{Pa}$. The option $2\times 10^{11}$ wrongly omits the factor of 0.5 in the strain. The option $1\times 10^{10}$ results from a units slip leaving volume in cm³. The option $5\times 10^{10}$ comes from inverting the strain ratio. A useful habit is to first compute the dimensionless volumetric strain and only then divide the pressure by it, which keeps the calculation transparent. As a magnitude check, the value lies in the typical range for stiff solids, far higher than that of gases which compress easily, and the units of pressure divided by a dimensionless strain correctly give pascals. The very small fractional volume change for such a large pressure also signals that the material is highly incompressible, consistent with a large bulk modulus.