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Question

A thick rope of rubber of density 1.5× 103 kg m3and Young’s modulus 5 × 106 N m2, 8m in length is hung from the ceiling of a room, the increase in its length due to its own weight is

A
9.6 X 10–2 m
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B
19.2 X 10–2 m
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C
9.6 X 10–3 m
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D
9.6 m
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Solution

The correct option is A 9.6 X 10–2 m

If A is the area of cross section, d be the density of material and l is length of rope
then mass of rope m=Ald
As the weight of the rope acts on the mid point of the rope
Y=mgA×l l
l=mgl2AY=Alpgl2AY=gpl22Y
or l=9.8 × 1.5 × 103 × 822 × 5 × 106=9.6×102m


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