Question

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

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

Answer 1

The correct option is D $9F$


$Stress=\frac{F}{A};Strain=\frac{\Delta x}{l}$

$Y=\frac{\text{Stress}}{\text{Strain}}$


$Y=\frac{Fl}{A\Delta x}$

$F=\frac{YA\Delta x}{l}\frac{\times A}{\times A}$

$F=\frac{Y{A}^2\Delta x}{v}$

$⟹F\propto A^2$

$⟹F^{\prime }\propto 9A^2$

$\frac{F^{\prime }}{F}=\frac{9A^2}{A^2}$

So, $F^{\prime }=9F$