Question

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:

• A. 2800
• B. 5600
• C. 8400
• D. 11200

Answer 1

The Correct Option is B

To calculate the energy per unit volume stored in an aluminium rod due to elastic strain, we use the formula for strain energy density, which is given by:

U = \frac{1}{2} \times \text{Stress} \times \text{Strain}

In terms of Young's modulus Y (also known as modulus of elasticity), the strain energy density formula can be expressed as:

U = \frac{1}{2} \times Y \times \text{Strain}^2

From the problem:

• Young's modulus, Y = 7.0 \times 10^{10}\, \text{N/m}^2
• Elastic strain, \text{Strain} = 0.04\% = 0.04/100 = 0.0004

Substituting these values into the formula, we get:

\begin{align*} U &= \frac{1}{2} \times 7.0 \times 10^{10} \times (0.0004)^2 \\ &= \frac{1}{2} \times 7.0 \times 10^{10} \times 0.00000016 \\ &= \frac{1}{2} \times 7.0 \times 10^{10} \times 1.6 \times 10^{-7} \\ &= \frac{1}{2} \times 11.2 \times 10^3 \\ &= 5600\, \text{J/m}^3 \end{align*}

Thus, the energy per unit volume stored in the aluminium rod is 5600 J/m³.

This matches the given correct option: 5600.