Question

Two wires are made of the same material and have the same volume . However wire 1 has cross section area A and wire 2 has cross-section area 3A . If the length of wire 1 increases by$△x$ on applying force F, how much force is needed to stretch wire 2 by the same amount ?

Answer 1

We know that-

$\Delta L=\frac{FL}{AY}=\frac{FV}{A^{2}Y}$ where volume$=V=AL$

$⟹F\propto A^2$ for same elongation

$⟹\frac{F_2}{F_1}={\left(\frac{A_2}{A_1}\right)}^2$

$⟹\frac{F_2}{F}={\left(\frac{3A}{A}\right)}^2$

$⟹F_2=9F$