Question

The ratio of diameters of two wires of same material is $n:1$. The length of wires are $4\text{m}$ each. On applying the same load, the increase in length of the thin wire will be

• A. $n^2\text{times}$
• B. $n\text{times}$
• C. $2n\text{times}$
• D. none of these

Answer 1

The correct option is A $n^2\text{times}$

$\Delta L=\frac{Fl}{AY}$

$\Delta l\alpha \frac{1}{A}\alpha \frac{1}{d^2}$

$\frac{\Delta l_1}{\Delta l_2}=\frac{d_2^2}{d_1^2}$

$\Delta l_2=n^2\Delta l_1$