## Q. 2.4

Obtain an expression for change in length of a freely hanging wire of diameter d and length l. Unit weight of the material of the wire is w.

## Verified Solution

We know that the change in length of a prismatic component (here, wire is also prismatic as it has the same cross sectional area over entire length) is given by

$d l=\frac{P l}{A E}$

where,
P = volume of wire × unit weight $=\frac{\pi d^2}{4} l w$

A = area of cross section =$\frac{\pi d^2}{4}$

Therefore, change in length = dl = $\frac{l^2 w}{E}$