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Q.

A rubber cord of length L is suspended vertically. Density of rubber is ρ and Young's modulus is Y. If the cord extends by a length ΔL under its own weight, then ΔL is,

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a

$\frac{ρ g L^{2}}{Y}$

b

$\frac{ρ g L^{2}}{2 Y}$

c

$\frac{ρ g L^{2}}{3 Y}$

d

$\frac{ρ g L^{2}}{4 Y}$

answer is B.

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Detailed Solution

$Y = \frac{\frac{m g}{A}}{\frac{∆ l}{\frac{l}{2}}} e f f e c t i v e l e n g t h l / 2 ∆ l = \frac{m g l}{2 A Y} = \frac{ρ l^{2} g}{2 Y} (m = l A ρ)$

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