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 $3A$. 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 $9F$

${\ell }_1=3{\ell }_2$ (given)
$Y=\frac{F}{A}\times \frac{{\ell }_1}{\Delta x}$ (i) [symbols have their usual meaning]
$Y=\frac{F^1}{3A}\times \frac{{\ell }_1/3}{\Delta x}$ (ii)
$\frac{F}{A}\times \frac{{\ell }_1}{\Delta x}=\frac{F^{\prime }}{3A}\times \frac{{\ell }_1}{3\Delta x}$
$F^{\prime }=9F$