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
A$\frac{ MgL }{ A \left( L _{1}- L \right)}$
B$\frac{ MgL _{1}}{ AL }$
C$\frac{ Mg \left( L _{1}- L \right)}{ AL }$
D$\frac{ MgL }{ AL _{1}}$
NEET 2020, Easy
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A$\frac{ MgL }{ A \left( L _{1}- L \right)}$
a $Y=\frac{F L }{A \Delta L}=\frac{M g L}{A\left(L_{1}-L\right)}$
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