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Q.

A wire of length L and density $ρ$ and Young's modulus Y is hanging from a support. Find the elongation in the length of wire at which wire will break:

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a

$\frac{L^{2} ρg}{Y}$

b

$\frac{L^{2} ρg}{2 Y}$

c

$\frac{2 L^{2} ρg}{Y}$

d

$\frac{L^{2} ρg}{4 Y}$

answer is A.

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Detailed Solution

$Y = \frac{S t r e s s}{S t r a i n} = \frac{σ l}{∆ l}$

$∆ l \frac{σL}{Y} = \frac{ALρg}{A} . \frac{L}{Y} = \frac{L^{2} ρg}{Y}$

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