Question

A cable stretches by an amount d when it supports a crate of mass M. The

cable is replaced by another cable of the same material having the same

length and twice the diameter. If the same crate is supported by the

thicker cable, by how much will the cable stretch?

Answer 1

$$\frac{A'}{A}=\frac{r'^2}{r^2}=\frac{(2r)^2}{r^2}=4$$

$$\frac{\sigma'}{\sigma}=\frac{A}{A'}=0.25$$

But

$$\frac{d'}{d}=\frac{\sigma'}{\sigma}=0.25$$

$$d'=0.25d$$