Question

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

• A. $n^2$
• B. n
• C. 2n
• D. $\sqrt{n}$

Answer 1

The correct option is A

$n^2$

Since $F$ , $L$ and $Y$ are constants,

$l\propto \frac{1}{A}\Rightarrow l\propto \frac{1}{d^2}$, where d is the diameter of the wire. Therefore,

$\frac{l_2}{l_1}={\left(\frac{d_1}{d_2}\right)}^2$

$=n^2$