Question

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

• A. 4F
• B. 6F
• C. 9F
• D. F

Answer 1

The correct option is C 9F

$Y=\frac{Fl}{A△l}$
so,$F=\frac{Y{A}^2△l}{Al}=\frac{Y{A}^2△l}{V}$
where,$Al=V=$ Volume of wire
hence $F\propto A^2$
$\frac{F^{\prime }}{F}=\frac{(3A{)}^2}{A^2}=9$
or F'=9F