Question:
Pressure of $2 \times 10^6$ Pa causes volume decrease of $0.1\%$ in a material. Bulk modulus is:
Pressure of $2 \times 10^6$ Pa causes volume decrease of $0.1\%$ in a material. Bulk modulus is:
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When the volume decrease is given as a percentage, the strain is simply $\frac{\% \text{ change}}{100}$. If $\Delta V/V$ is $10^{-n}$, the exponent of $10$ in the result will increase by $n$.
Updated On: May 20, 2026
- $2 \times 10^9$ Pa
- $2 \times 10^{10}$ Pa
- $1 \times 10^{10}$ Pa
- $5 \times 10^9$ Pa
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The Correct Option is A
Solution and Explanation
Concept:
The problem relates to the elastic properties of matter. The Bulk modulus ($B$) is defined as the ratio of volumetric stress (pressure) to volumetric strain. It is a measure of how resistant a substance is to compression.
\[ B = \frac{\Delta P}{-\frac{\Delta V}{V}} \]
Where:
• $\Delta P$ is the change in pressure.
• $\frac{\Delta V}{V}$ is the volumetric strain (fractional change in volume).
Step 1: Identify the given values.
From the question:
• Pressure ($\Delta P$) = $2 \times 10^6$ Pa
• Percentage decrease in volume = $0.1\%$ Calculating volumetric strain ($\frac{\Delta V}{V}$): \[ \frac{\Delta V}{V} = \frac{0.1}{100} = 10^{-3} \]
Step 2: Calculate the Bulk Modulus.
Using the formula: \[ B = \frac{\Delta P}{\frac{\Delta V}{V}} \] \[ B = \frac{2 \times 10^6}{10^{-3}} \] \[ B = 2 \times 10^6 \times 10^3 \] \[ B = 2 \times 10^9 \text{ Pa} \]
• $\Delta P$ is the change in pressure.
• $\frac{\Delta V}{V}$ is the volumetric strain (fractional change in volume).
Step 1: Identify the given values.
From the question:
• Pressure ($\Delta P$) = $2 \times 10^6$ Pa
• Percentage decrease in volume = $0.1\%$ Calculating volumetric strain ($\frac{\Delta V}{V}$): \[ \frac{\Delta V}{V} = \frac{0.1}{100} = 10^{-3} \]
Step 2: Calculate the Bulk Modulus.
Using the formula: \[ B = \frac{\Delta P}{\frac{\Delta V}{V}} \] \[ B = \frac{2 \times 10^6}{10^{-3}} \] \[ B = 2 \times 10^6 \times 10^3 \] \[ B = 2 \times 10^9 \text{ Pa} \]
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