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 :
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 :
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Bulk modulus \(K = \frac{P}{\Delta V/V}\) and for fixed mass \(\frac{\Delta\rho}{\rho} = \frac{\Delta V}{V}\) in magnitude.
Updated On: Nov 4, 2026
- \(\frac{\rho K}{P}\)
- \(\frac{PK}{\rho}\)
- \(\frac{\rho P}{K}\)
- \(\frac{K}{\rho P}\)
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The Correct Option is C
Solution and Explanation
Bulk modulus \(K = \frac{P}{|\Delta V|/V}\), so \(\frac{|\Delta V|}{V} = \frac{P}{K}\).
Mass is fixed: \(\rho V = \text{constant}\), so \(\frac{\Delta\rho}{\rho} = -\frac{\Delta V}{V}\), giving \(\left|\frac{\Delta\rho}{\rho}\right| = \frac{P}{K}\).
\(\Delta\rho = \frac{\rho P}{K}\).
Answer: (3) \(\frac{\rho P}{K}\)
Mass is fixed: \(\rho V = \text{constant}\), so \(\frac{\Delta\rho}{\rho} = -\frac{\Delta V}{V}\), giving \(\left|\frac{\Delta\rho}{\rho}\right| = \frac{P}{K}\).
\(\Delta\rho = \frac{\rho P}{K}\).
Answer: (3) \(\frac{\rho P}{K}\)
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