A wire of original length $L$ and Young's modulus $Y$ is hanging from a fixed support. When a mass $

Question

A wire of original length $L$ and Young's modulus $Y$ is hanging from a fixed support. When a mass $M$ is suspended from its free end, its new length becomes $L_1$. The expression for the cross-sectional area $A$ of the wire is

Professor PC Thomas Classes · Answer

Let the original length be $L$ and the new length be $L_1$. The change in length is $\Delta L = L_1 - L$. The restoring force is the weight $F = Mg$. Young's modulus is defined as $Y = \frac{	ext{Stress}}{	ext{Strain}} = \frac{F/A}{\Delta L / L} = \frac{MgL}{A(L_1 - L)}$. Rearranging this formula to solve for the cross-sectional area $A$ yields $A = \frac{MgL}{Y(L_1 - L)}$.