Question

A material has normal density $\rho$ bulk modulus $B$ . The increase in the density of the material, when it is subjected to an external pressure $P$ from all sides is:

Answer 1

Hint: In order to answer this question, we have to know the increase in the density of the given material, we will first find the equation having increase in density by the help of the formula of Bulk Modulus and then we will discuss more about the bulk modulus.

Complete step by step answer:
Bulk Modulus:
$$\begin{gathered} B={\displaystyle \frac{-P}{\mathrm{\Delta }V/V}}={\displaystyle \frac{-P}{-\mathrm{\Delta }\rho /{\rho }^2}} \\ \Rightarrow \mathrm{\Delta }\rho ={\displaystyle \frac{P{\rho }^2}{B}}=increaseindensity \end{gathered}$$
A substance's bulk modulus is a measurement of how robust it is to compression. It's the ratio of the infinitesimal pressure rise to the volume's corresponding relative decrease.
The bulk modulus of elasticity is one of the mechanical properties of solids that can be measured. Young's modulus and Shear modulus are two other elastic modules. In any case, a material's bulk elastic properties are used to calculate how much it can compress when subjected to a specified amount of external pressure.

Note: For solids and liquids, this variation is usually small, but for gases, it is much greater. When you apply more pressure to an object, it shrinks in volume and thus becomes denser. With a few exceptions, increasing the temperature of a material reduces its density by increasing its volume.