# A rubber string 10 m long is suspended from a rigid support at one end. Calculate extension

10.8k views
in Physics

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 Yrubber = 5 × 106Nm-2.

+1 vote
by (55.0k points)
selected

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.