The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of 7 × 10⁶ Pa, would be __________ mm ³.
(Given bulk modulus of copper =1.4 × 10¹¹ N m⁻² )

Solution

Physics sir · 4 steps

Bulk modulus gives Δ V = PV/B directly, then cube the length factor to reach mm³.

1. Bulk modulus. The bulk modulus is the pressure divided by the fractional change in volume, B = P/(Δ V / V). Rearranging gives the contraction directly.

   Δ V = (P V)/B

2. Volume of cube. The edge is 10 cm = 0.1 m, so V = (0.1)³ = 1 × 10⁻³ m³.
3. Put in numbers. Δ V = (7 × 10⁶ × 1 × 10⁻³)/(1.4 × 10¹¹) = 5 × 10⁻⁸ m³.
4. So. Since 1 m = 10³ mm, 1 m³ = 10⁹ mm³. That gives Δ V = 5 × 10⁻⁸ × 10⁹ = 50 mm³, so the answer is 50.

The common slip: 0.05. Converting m³ to mm³ with 10⁶ instead of 10⁹ gives 0.05, not 50. The length factor 10³ must be cubed.

The idea to keep. For any solid under uniform pressure, Δ V / V = P/B. Work in SI units, and when converting volumes cube the length factor: 1 m³ = 10⁹ mm³.

Answer from the NTA final answer key. Solution by PrepWiser.