PYQ NEET- Mechanical Properties Of Solids L-4

Question: A wire of length $L$, area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L$, when mass $M$ is suspended from its free end. The expression for Young’s modulus is#

A) $\frac{M g\left(L_1-L\right)}{A L}$

B) $\frac{M g L}{A L_1}$

C) $\frac{M g L}{A\left(L_1-L\right)}$

D) $\frac{M g L_1}{A L}$

Answer: $\frac{M g L}{A\left(L_1-L\right)}$#

Sol:#

Here, change in length, $\Delta L=\left(L_1-L\right)$ Area $=A$ Force, $F=M g$ Young’s modulus, $Y=\frac{\text { Normal stress }}{\text { Longitudinal strain }}$ $$ \begin{aligned} \Rightarrow \quad Y & =\frac{(F / A)}{\left(\frac{\Delta L}{L}\right)}=\frac{\frac{M g}{A}}{\left(\frac{L_1-L}{L}\right)} \ & =\frac{M g L}{A\left(L_1-L\right)} \end{aligned} $$

Hence, correct option is (c).