Question 12 of 13intermediate🔧 ApplyNumerical4 marks

Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0×107.0 \times 10⁶ Pa.

Correct Answer

The volume contraction of the solid copper cube is 5×105 \times 10⁻⁸ m³ (or 0.05 cm³).

Exercise: EXERCISES | Q: 8.15
For More Understanding

Explanation

This numerical problem from NCERT Chapter 8 (Mechanical Properties of Solids) applies the concept of bulk modulus. The bulk modulus (B) relates hydraulic pressure to volumetric strain through the relation B = -P/(ΔV/V). The negative sign indicates volume decreases under pressure. The original volume of the cube is V = L³ = (10 cm)³ = 1000 cm³ = 10⁻³ m³. Using the bulk modulus of copper (B = 140×10140 \times 10⁹ Pa from NCERT material property tables), the volume contraction is calculated.

Solution Steps

  1. Step 1: Calculate original volume: V = L³ = (0.1 m)³ = 10⁻³ m³

  2. Step 2: Apply bulk modulus formula rearranged for volume change: ΔV = P × V / B

  3. Step 3: Substitute values: ΔV = (7.0×107.0 \times 10⁶ Pa × 10⁻³ m³)/(140×10140 \times 10⁹ Pa)

  4. Step 4: Solve: ΔV = 7.0×107.0 \times 10³/(140×10140 \times 10⁹) = 5×105 \times 10⁻⁸ m³ = 0.05 cm³

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