Question

An elastic material with Young's modulus $Y$ is subjected to a tensile stress $S$. The elastic energy stored per unit volume of the material will be

• A. $\dfrac{S^2}{Y}$
• B. $\dfrac{S^2}{2Y}$
• C. $\dfrac{YS}{2}$
• D. $\dfrac{S}{2Y}$

Hint:

Elastic energy density depends on the square of stress and inversely on Young’s modulus.

Answer 1

The Correct Option is B

Step 1: Write expression for elastic energy density.
Elastic energy stored per unit volume is given by:
\[ u = \frac{1}{2} \times \text{stress} \times \text{strain} \]

Step 2: Use relation between stress and strain.
\[ \text{strain} = \frac{S}{Y} \]

Step 3: Substitute values.
\[ u = \frac{1}{2} \times S \times \frac{S}{Y} = \frac{S^2}{2Y} \]

Step 4: Conclusion.
The elastic energy stored per unit volume is $\dfrac{S^2}{2Y}$.