Chapter 2
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.
Step-by-Step
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}