Question

A wire stretches by a certain amount under a load. If the load & radius both are increased to $4$ time . Find the stress cause in the wire.

Answer 1

Young's modulus $\gamma =\frac{W}{A}\times \frac{L}{l}$

Elongation $l=\frac{WL}{A\gamma }$

Elongation $l=\frac{WL}{\pi r^2\gamma }.....\left(1\right)$ $(\because A=\pi r^2)$

When both load and radius are increased to four times, the elongation becoems,

$l^{\prime }=\frac{4WL}{(4r{)}^2\pi \gamma }$

$l^{\prime }=\frac{WL}{4\pi r^2\gamma }$

So, from (1)

$l^{\prime }=\frac{l}{4}$