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 :

Properties of Matter PYQ — JEE Main 2021 · 26 Feb · Shift 1 · Q60 with Solution

View written solutionFree

Correct answer: C

Bulk modulus is defined as

K = -\frac{P}{\Delta V/V}

where $P$ is the applied pressure and $\Delta V$ is the change in volume.

For magnitude, we write

\frac{\Delta V}{V} = \frac{P}{K}

Since pressure compresses the material, volume decreases.

Density is

\rho = \frac{m}{V}

Since mass remains constant, a small decrease in volume causes density to increase.

For small changes,

\rho' = \frac{m}{V-\Delta V}

Using fractional change,

\frac{\Delta \rho}{\rho} = \frac{\Delta V}{V}

in magnitude.

More precisely, because $\rho \propto \frac{1}{V}$ ,

\frac{\Delta \rho}{\rho} = -\frac{\Delta V}{V}

So in magnitude,

\frac{\Delta \rho}{\rho} = \frac{P}{K}

Thus,

\Delta \rho = \rho \cdot \frac{P}{K}

So the magnitude of increase in density is

\boxed{\frac{\rho P}{K}}

Therefore, the correct option is C.