Question

A wire of cross-section area $2{\text{mm}}^2$ is stretched by $0.1\text{mm}$ by a certain force. How far (length) will the wire of same material and length but area $8{\text{mm}}^2$ stretch under the action of same force?

• A. $0.25\text{mm}$
• B. $0.005\text{mm}$
• C. $0.025\text{mm}$
• D. $0.05\text{mm}$

Answer 1

The correct option is C $0.025\text{mm}$

Given:
Area of 1st wire; $A_1=2\times {10}^{-6}{\text{mm}}^2$
Area of 2nd wire; $A_2=8\times {10}^{-6}{\text{mm}}^2$
$\Delta L_1=0.1\times {10}^{-3}\text{m}$
As length, force on wire and material of wire are same.
$\therefore L_1=L_2,F_1=F_2,Y_1=Y_2$
We know,
$\Delta L=\frac{FL}{AY}$
$\therefore \Delta L_1=\frac{F_1{L}_1}{A_1{Y}_1}$
Simillarly
$\Delta L_2=\frac{F_2{L}_2}{A_2{Y}_2}$
$\therefore \frac{\Delta L_2}{\Delta L_1}=\frac{A_1}{A_2}=\frac{2}{8}$
$\Rightarrow \Delta L_2=\frac{1}{4}\times 0.1\times {10}^{-3}\text{m}=0.025\text{mm}$