MHT CET · Physics · Kinetic Theory of Gases
If in a wire of Young's modulus \(Y\), longitudinal strain \(X\) is produced then the potential energy stored in its unit volume will be
- A \(0.5 Y X^{2}\)
- B \(0.5 Y^{2} X\)
- C \(2 Y X^{2}\)
- D \(Y X^{2}\)
Answer & Solution
Correct Answer
(A) \(0.5 Y X^{2}\)
Step-by-step Solution
Detailed explanation
When a wire is stretched work is done against the interatomic forces. This work is stored in the wire in the form of elastic potential energy. Elastic potential energy per unit volume is
\(
U=\frac{1}{2} \times \text { stress } \times \text { strain }
\)
From definition of Young's modulus of wire
\(
\begin{aligned}
Y &=\frac{\text { stress }}{\text { strain }} \\
\Rightarrow \quad \text { Stress } &=Y \times \text { strain }
\end{aligned}
\)
Given, \(\quad\) strain \(=X\)
Therefore, \(U=\frac{1}{2} Y X^{2}\)
\(
\Rightarrow \quad U=0.5 Y X^{2}
\)
\(
U=\frac{1}{2} \times \text { stress } \times \text { strain }
\)
From definition of Young's modulus of wire
\(
\begin{aligned}
Y &=\frac{\text { stress }}{\text { strain }} \\
\Rightarrow \quad \text { Stress } &=Y \times \text { strain }
\end{aligned}
\)
Given, \(\quad\) strain \(=X\)
Therefore, \(U=\frac{1}{2} Y X^{2}\)
\(
\Rightarrow \quad U=0.5 Y X^{2}
\)
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