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A thick rope of density ρ and length L is hung from a rigid support. The Young’s modulus of the material of rope is Y. The increase in length of the rope due to its own weight is

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a

ρgL24Y

b

ρgL22Y

c

ρgL2Y

d

ρgLY

answer is B.

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Detailed Solution

Δℓ=F(L/2)AY=(ALρg)(L)2AY=ρgL22Y

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