Question

A steel wire of diameter 3.6 x 10^-4 m and length 4m extends by 1.8 x 10^-3 m under a load of 1 kg and twists by 1.2 radians when subjected to a total torsional torque of 8.4 x 10^-5 Nm at one end. Find the values of Young’s and rigidity modulus

Answer 1

The Young's modulus:

$$Y=\frac{\Delta L}L·\frac FA=43.3\text{ kPa}.$$

The rigidity modulus:

$$G=\frac {TL}\theta=\frac {(8.4·10^{-5})·4}{1.2}=2.8·10^{-4}\text{ N}·\text {m}^2/\text{rad}$$