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

Step 1: Recall the Energy Density Formula
 The energy per unit volume \( u \) is given by: \[ u = \frac{1}{2} \cdot \text{stress} \cdot \text{strain} \] We also know: \[ \text{stress} = Y \cdot \text{strain} \] 
Step 2: Substitute the Values 
Given: \[ Y = 7.0 \times 10^{10} \, \text{N/m}^2, \quad \text{strain} = \frac{0.04}{100} = 0.0004 \] Substitute these values into the formula: \[ u = \frac{1}{2} \cdot Y \cdot (\text{strain})^2 \] \[ u = \frac{1}{2} \cdot 7.0 \times 10^{10} \cdot (0.0004)^2 \] \[ u = 5600 \, \text{J/m}^3 \]
 Final Answer
 The energy per unit volume is: \[ u = 5600 \, \text{J/m}^3 \]