Question

what is the force required for a steel wire to double its length when its area of cross section is one square cm and young modules is 200G pa.as the length of the wire is doubled the change in length is equal to its original length

Answer 1

Given:

$\varepsilon=1$

$E=200\:\rm GPa$

$A=1\:\rm cm^2=10^{-4}\:\rm m^2$

The stress is given by

$$\sigma=\frac{F}{A}=\varepsilon E$$

Hence, the force required for a steel wire to double its length

$$F=\varepsilon E A=1*200*10^9*10^{-4}=2*10^7\:\rm N$$