Question

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A$. If length of the first wire is increased by $\Delta l$ on applying a force $F$, then how much force is needed to stretch the second wire by the same amount?

• A. $9F$
• B. $6F$
• C. $4F$
• D. $F$

Answer 1

The correct option is A $9F$

$Y=\frac{Fl}{A\Delta l}F=\frac{YA\Delta l}{l}=\frac{Y{A}^2\Delta l}{V}\left(\because V=Al\right)\therefore \frac{F_1}{F_2}={\left(\frac{A_1}{A_2}\right)}^2={\left(\frac{A}{3A}\right)}^2=\frac{1}{9}\Rightarrow F_2=9F_1=9F$