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JEE MAIN 2021
26-02-2021 S1
Question
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 :
Select the correct option:
A
$\frac{\rho \mathrm{K}}{\mathrm{P}}$
B
$\frac{\rho \mathrm{P}}{\mathrm{K}}$
C
$\frac{\mathrm{K}}{\rho \mathrm{P}}$
D
$\frac{\text { PK }}{\rho}$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\begin{aligned} & \rho=\frac{M}{V} \\ & \frac{d \rho}{\rho}=-\frac{d V}{V} \\ & k=-\frac{P}{\frac{d V}{V}} \\ & -\frac{d V}{V}=\frac{P}{k} \\ & \frac{d \rho}{\rho}=\frac{P}{k} \Rightarrow d \rho=\frac{\rho P}{k}\end{aligned}$
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