Question

A cable stretches by an amount x under a certain load. if it is replaced by a cable of the same material but half as long and half the diameter, the same load will stretch it by ?

Answer 1

Young's modulus is

$$E=\frac{FL}{Ax}=\frac{0.5LF}{A'x'}$$

$$\frac{FL}{\pi r^2x}=\frac{0.5LF}{\pi (0.5r)^2x'}$$

$$x'=2x$$