A thick uniform rubber rope of density 1.5 gcm−3 and Young's modulus 5×106 Nm−2 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
9.6×10−2 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 cm−3=1500 kgm−3,
∴l=10×(8)2×15002×5×106=9.6×10−2 m
Hence, the correct choice is (a).