A material has normal density ρ and bulk modulus K. The increase in the density of the material when it is…

Q: A material has normal density ρ and bulk modulus K. The increase in the density of the material when it is subjected to an external pressure P from all sides is

(a) \displaystyle \frac{P}{\rho K}

(b) \displaystyle \frac{K P}{\rho }

(c) \displaystyle \frac{P \rho}{ K}

(d) \displaystyle \frac{K \rho}{P}

Ans: (c)

\displaystyle \rho = \frac{M}{V}

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

Bulk Modulus of Elasticity is

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

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

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

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

Author: Rajesh Jha

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