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Question

A thick uniform rubber rope of density 1.5 gcm3 and Young's modulus 5×106 Nm2 has a length of 8 m. When hung from the ceiling of a room, the increase in length of the rope due to its own weight will be equal to


A

9.6×102 m

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B

19.2×103 m

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C

9.6×103 m

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D

9.6 m

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Solution

The correct option is A

9.6×102 m


The weight of the rope can be assumed to act at its mid-point. Now, the extension l is proportional to original length L. If the weight of the rope acts at its mid-point, the extension will be that produced by half the rope. So, replacing L by L2 in the expression for Young's modulus, we have
Y=FL2Al=FL2Al
l=FL2AY=ρALg×L2AY=gL2ρ2Y
Now, ρ=1.5g cm3=1500 kgm3,
l=10×(8)2×15002×5×106=9.6×102 m
Hence, the correct choice is (a).


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