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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 $M_{1}$ is suspended from its free end. The length changes to $L_{2}$ when $M_{2}$ is also suspended. Young's modulus of the material is

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$\frac{M_{1} g L}{A (L_{2} - L_{1})}$

$\frac{M_{1} g L}{(L_{1} + L_{2}) A}$

$\frac{M_{2} g L}{(L_{2} - L_{1}) A}$

$\frac{M_{2} g L}{(L_{1} + L_{2}) A}$

answer is C.

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Detailed Solution

$\frac{M_{1} g}{A Y} = \frac{L_{1} - L}{L} \frac{(M_{1} + M_{2}) g}{A Y} = \frac{L_{2} - L}{L} S u b t r a c t i n g a b o v e t w o q u e s t i o n s, \frac{M_{2} g}{A Y} = \frac{L_{2} - L_{1}}{L} \frac{M_{2} g L}{(L_{2} - L_{1}) A} = Y$

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