Q.A solid metal sphere of volume 0.31 m³ is dropped in an ocean where the water pressure is 2×10⁷ N/m². Calculate the change in volume of the sphere if the bulk modulus of the metal is 6.1×10¹⁰ N/m².

Bulk modulus $K$ is the modulus of elasticity associated with a change in the volume of a body under an applied deforming force — the elasticity of volume. Unlike Young's modulus and the modulus of rigidity, which apply only to solids, bulk modulus is a property shared by solids, liquids and gases, since all three states of matter have a definite volume.

For a body of original volume $V$ subjected to a volume stress $dP$ that produces a volume change $dV$, the volume strain is defined as $-dV/V$ (the minus sign ensures the strain is reported as a positive quantity even though $dV$ itself is negative for a pressure increase), and the bulk modulus is

Its SI unit is $\text{N/m}^2$, dimensional formula $[L^{-1}M^1T^{-2}]$. Its reciprocal, $1/K$, is called compressibility — the fractional decrease in volume per unit increase in pressure — measured in $\text{Pa}^{-1}$. …