Question

An Indian rubber card 10 m long is suspended vertically. How much does it stretch under its own weight? Density of rubber = 1.5 x 10³ kg m^-3 and Young's modulus of rubber = 6 x 10⁶ g f cm^-2

Answer 1

Here, L = 10 m;

ρ = 1.5 x 10³ kg^-3

Y = 6 x 10⁶ g f cm^-2

= 6 x 10⁶ x 980 dyne cm^-2

= 5.88 x 10⁸ Nm^-2

Let 'a' be the area of cross-section of the Indian rubber cord. Then,

F = weight of the rubber cord

= L x a x ρ x g

The weight of the rubber cord acts at its centre of gravity and hence the weight of the rubber cord will produce extension in the length L/2 of the cord.

Now, Y = {F(L/2)}/al

l = {F x L}/{2a x Y} = {L x a x ρ x g x L}/{2a x Y}

= {L²ρg}/{2Y} = {10² x 1.5 x 10³ x 9.8}/{2 x 5.88 x 10⁸}

= 1.25 x 10^-3 m = 1.25 mm