Question:
A metal cube has edge length 0.1 m. The bulk modulus of the metal is \(1.4 \times 10^{11} \, \text{N/m}^2\). When subjected to hydraulic pressure, the volume contraction of the cube is \(5 \times 10^{-2} \, \text{cm}^3\). The applied pressure is
A metal cube has edge length 0.1 m. The bulk modulus of the metal is \(1.4 \times 10^{11} \, \text{N/m}^2\). When subjected to hydraulic pressure, the volume contraction of the cube is \(5 \times 10^{-2} \, \text{cm}^3\). The applied pressure is
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Always convert cm³ to m³ before applying bulk modulus formula.
Updated On: Jun 20, 2026
- \(2 \times 10^6 \, \text{Pa}\)
- \(1.4 \times 10^7 \, \text{Pa}\)
- \(7 \times 10^6 \, \text{Pa}\)
- \(5 \times 10^5 \, \text{Pa}\)
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The Correct Option is C
Solution and Explanation
Step 1: Bulk modulus formula.
\[ B = \frac{P}{\Delta V / V} \Rightarrow P = B \cdot \frac{\Delta V}{V} \]
Step 2: Find original volume.
\[ V = (0.1)^3 = 10^{-3} \, \text{m}^3 \]
Step 3: Convert volume change.
\[ \Delta V = 5 \times 10^{-2} \, \text{cm}^3 = 5 \times 10^{-8} \, \text{m}^3 \]
Step 4: Compute strain.
\[ \frac{\Delta V}{V} = \frac{5 \times 10^{-8}}{10^{-3}} = 5 \times 10^{-5} \]
Step 5: Calculate pressure.
\[ P = 1.4 \times 10^{11} \times 5 \times 10^{-5} \] \[ P = 7 \times 10^6 \, \text{Pa} \]
Step 6: Final answer.
\[ \boxed{7 \times 10^6 \, \text{Pa}} \]
\[ B = \frac{P}{\Delta V / V} \Rightarrow P = B \cdot \frac{\Delta V}{V} \]
Step 2: Find original volume.
\[ V = (0.1)^3 = 10^{-3} \, \text{m}^3 \]
Step 3: Convert volume change.
\[ \Delta V = 5 \times 10^{-2} \, \text{cm}^3 = 5 \times 10^{-8} \, \text{m}^3 \]
Step 4: Compute strain.
\[ \frac{\Delta V}{V} = \frac{5 \times 10^{-8}}{10^{-3}} = 5 \times 10^{-5} \]
Step 5: Calculate pressure.
\[ P = 1.4 \times 10^{11} \times 5 \times 10^{-5} \] \[ P = 7 \times 10^6 \, \text{Pa} \]
Step 6: Final answer.
\[ \boxed{7 \times 10^6 \, \text{Pa}} \]
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