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 $\triangle l$ on applying a force F, how much force is needed to stretch the socond wire by the same amount?
4 F
6 F
9 F
F
Explanation:
For wire 1,
$\triangle l =\left(\dfrac{F}{AY}\right)3l \cdot\cdot\cdot(i)$
For wire 2,
$\dfrac{\acute{F}}{3A}=Y\dfrac{\triangle l}{l}$
$\triangle l =\left(\dfrac{\acute{F}}{3AY}\right)l \cdot\cdot\cdot(ii)$
From equation (i) & (ii),
$ \triangle l= \left(\dfrac{F}{AY}\right)3l= \left(\dfrac{\acute{F}}{3AY}\right)l$
$\Rightarrow \acute{F}=9F$
For wire 1,
$\triangle l =\left(\dfrac{F}{AY}\right)3l \cdot\cdot\cdot(i)$
For wire 2,
$\dfrac{\acute{F}}{3A}=Y\dfrac{\triangle l}{l}$
$\triangle l =\left(\dfrac{\acute{F}}{3AY}\right)l \cdot\cdot\cdot(ii)$
From equation (i) & (ii),
$ \triangle l= \left(\dfrac{F}{AY}\right)3l= \left(\dfrac{\acute{F}}{3AY}\right)l$
$\Rightarrow \acute{F}=9F$
