Solids: Practice Problem & Solution
A wire of length $L$ area of cross section $A$ is hanging from a fixed support. The length of the wire changes to $L_1$ when mass $M$ is suspended from its free end. The expression for Young's modulus is: (2020)
Solution Explained:
To solve this problem, we apply the core principles of Solids. Understanding the underlying formula is key to arriving at the correct answer below:
Young's modulus $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{Mg/A}{\Delta L/L}$. Here, the change in length $\Delta L = L_1 - L$. Substituting this gives $Y = \frac{MgL}{A(L_1 - L)}$.
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