A thick rope of rubber of density 1.5× 103 kg m−3and Young’s modulus 5 × 106 N m−2, 8m in length is hung from the ceiling of a room, the increase in its length due to its own weight is
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=9.6×10−2m