question_answer

A wire stretches by a certain amount under a load. If the load and radius both are increased to four times, find the stretch caused in the wire.

Answer:

                  Young's modulus, \[\Upsilon =\frac{W}{A}\times \frac{L}{l}\] \[\therefore \] Elongation, \[l=\frac{WL}{A\Upsilon }=\frac{WL}{\pi {{r}^{2}}\Upsilon }\] When both load and radius are increased to four times, the elongation becomes \[l'=\frac{4W\times L}{\pi {{(4r)}^{2}}\Upsilon }=\frac{WL}{4\pi {{r}^{2}}\Upsilon }=\frac{l}{4}.\]