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 the length of the first wire is increased by $\Delta l$ on applying a force $F$, how much force is needed to stretch the second wire by the same amount ?

• A. $4\text{F}$
• B. $6\text{F}$
• C. $9\text{F}$
• D. $\text{F}$

Answer 1

The correct option is C $9\text{F}$

Increase in length of wire of cross-sectional area $A$, when stretched by force $F$ is given by
$\Delta l=\frac{FL}{AY}=\frac{FV}{A^{2}Y}$ as $V=AL$.

As $Y$ and $V$ are constants, and $\Delta l$ should be same

$F\propto A^2$

Let $F^{\prime }$ be force needed to stretch the second wire. Then,

$\frac{F^{\prime }}{F}=\left(\frac{A_2^2}{A_1^2}\right)=9\Rightarrow F_2=9F$