A rubber rope of length 8 m is hung from the ceiling of a room. What is the increase in length of rope due to its own weight? (Young's modulus of elasticity of rubber = 5×106 Nm-2 and density of rubber = 1.5 × 103 kg m-3. Take g = 10 ms-2 )

Y = MgA×L2∆L( Length is taken as L2 because weight acts at C.G.)Now, M = ALρ[For the purpose of calculating mass, the whole of geometrical length L is to be considered]Y = ALρgL2A∆Lor ∆L = ρgL22Y = 1.5×103×10×8×82×5×106m         = 9.6 × 10-2 m = 9.6×10-2×103 mm          = 96 mm