The normal density of a material is $$\rho$$ and its bulk modulus of elasticity is $$K$$. The magnitude of increase in density of material, when a pressure $$P$$ is applied uniformly on all sides, will be:

The bulk modulus of elasticity is defined as $$K = -V \frac{dP}{dV}$$, which can be rewritten as $$\frac{dV}{V} = -\frac{P}{K}$$ for a pressure increase $$P$$.

Since mass is conserved, $$\rho V = \text{constant}$$. Differentiating, $$V \, d\rho + \rho \, dV = 0$$, which gives $$d\rho = -\frac{\rho \, dV}{V}$$.

Substituting $$\frac{dV}{V} = -\frac{P}{K}$$, we get $$d\rho = -\rho \times \left(-\frac{P}{K}\right) = \frac{\rho P}{K}$$.

Therefore, the magnitude of increase in density is $$\Delta\rho = \frac{\rho P}{K}$$.

Hence the correct answer is Option 2: $$\frac{\rho P}{K}$$.