Mechanical Properties of Solids - Result Question 1
1. 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]
(a) $\frac{Mg(L_1-L)}{AL}$
(b) $\frac{MgL}{AL_1}$
(c) $\frac{MgL}{A(L_1-L)}$
(d) $\frac{MgL_1}{AL}$
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Solution:
- (c) Stress $=\frac{\text{ force }}{\text{ cross-section area }}=\frac{M g}{A}$
Strain $=\frac{\text{ change in length }}{\text{ original length }}=\frac{\Delta L}{L}=\frac{L_1-L}{L}$
Young’s modulus, $Y=\frac{\text{ stress }}{\text{ strain }}=\frac{M g L}{A(L_1-L)}$
