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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

ρgL2Y

b

ρgL22Y

c

ρgL23Y

d

ρgL24Y

answer is B.

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Detailed Solution

Y=mgA∆ll2effective length l/2 ∆l=mgl2AY =ρl2g2Y  (m=lAρ)
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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,