An Indian rubber cord L metre long and area of cross-section A metre2 is suspended vertically. Density of rubber is p kg/metre3 and Young's modulus of rubber is Y newton/metre2. If the cord extends by l metre under its own weight, then extension I is

Weight of the cordW=Vρg=ALρg∴  Stress =WA=LρgFor the purpose of extension, the weight acts at the centre of gravity of the bar. Hence the upper half length, i.e., [L / 2) will be stretched.∴  Strain =l(L/2)=2lLNow, Y= Stress  Strain =Lρg×L2l=L2ρg2lor l=L2ρg/2Y