Question

The length of wire increases by 9 mm when weight of 2.5 kg is hung from the free end of wire. If all conditions are kept the same and the radius of wire is made thrice the original radius, find the increase in length.

Answer 1

Using $Y=\frac{FL}{A\Delta L}$

where $A=\pi r^2$

So, $\Delta L\propto \frac{1}{r^2}$

So, $\frac{\Delta L^{\prime }}{\Delta L}=\frac{r^2}{r^{\prime 2}}$

Or $\frac{\Delta L^{\prime }}{9}=\frac{r^2}{(3r{)}^2}=\frac{1}{9}$

$⟹\Delta L^{\prime }=1mm$