Question

Compute the extension in length of a wire 530 cm long and a diameter of 0.25 cm. When the body of mass 540 gm is applied vertically. The young modulus of given wire is 5x109 Dyne/cm2.

Answer 1

The area is

$$A=\frac{\pi d^2}{4}.$$

5·10⁹ Dyne/cm² is 5·10⁸ Pa.

Find the stress:

$$\sigma=\frac FA=\frac{mg}{A}.$$

The strain:

$$\epsilon=\frac{\Delta l}{l}\rightarrow\Delta l=\epsilon l.$$

And the Young's modulus is

$$E=\frac\sigma\epsilon\rightarrow\epsilon=\frac\sigma E\rightarrow\Delta l=\frac\sigma El,\\\space\\ \Delta l=\frac{4mg}{\pi d^2E}l=1.14\text{ cm}.$$