Question

A rubber string 10 m long is suspended from a rigid support at one end. Calculate extension of the string due to its own weight. The density of rubber is 1.5 × 10³ kg/m³ and Y_rubber = 5 × 10⁶Nm^-2.

Answer 1

The weight at any point x from below is, \(\frac {M}{10}\) (10 - x) where M is mass of string.

So, Force at any point dx is

F = \(\frac{Mg}{l}\) (l - x)dx

We know that,

Net extension =

So, Net extension of the rubber due to its own weight 

= \(\frac{1.5 \times 10^3 \times 10 \times 100}{2 \times 5 \times 10^{6}}\)

= 0.15 m.