An aluminium rod with Young's modulus Y=7.0 × 10¹⁰ N / m² undergoes elastic strain of 0.04 %. The energy per unit volume stored in the rod in SI unit is:

Solution

Physics sir · 4 steps

Energy stored per unit volume is half of stress times strain; turn the percent into a pure number first.

1. Energy density formula. For a wire stretched within the elastic limit, energy per unit volume is 1/2 × stress × strain. Since stress = Y × strain, this becomes the equation below.

   u = 1/2 Y (strain)²

2. Convert the strain. A strain of 0.04% means 0.04/100 = 4 × 10⁻⁴. Squaring gives (strain)² = 16 × 10⁻⁸ = 1.6 × 10⁻⁷.
3. Put in numbers. u = 1/2 × 7.0 × 10¹⁰ × 1.6 × 10⁻⁷ = 1/2 × 1.12 × 10⁴ = 5600 J m⁻³.
4. So. The energy stored per unit volume is 5600 J m⁻³, which is option (a).

The idea to keep. Elastic energy density is 1/2Y(strain)². Always change a percent strain into a decimal before squaring, and do not forget the 1/2.

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