Question

The ratio of diameters of two wires of same materials is $n: 1$. The length of each wire is $4 \,m$. On applying the same load, the increase in length of thin wire will be $(n > 1)$

• A. $n^{2}$ times
• B. $n$ times
• C. $2 n$ times
• D. $(2 n+1)$ times

Answer 1

Answer: (A)

As, $Y=\frac{\frac{\frac{l}{A}}{\Delta l}}{l}=\frac{F l}{A \Delta l}$
or $Y=\frac{F l \times 4}{\pi D^{2} \times \Delta l}$
or $\Delta l \propto \frac{1}{D^{2}}$
or $\frac{\Delta L_{2}}{\Delta L_{1}}=\frac{D_{1}^{2}}{D_{2}^{2}}=\frac{n^{2}}{1}$