Question

The following four wires of length $L$ and radius $r$ are made of the same material. When they are under same tension, the largest extension is produced in

• A. $L=200cm,r=0.5mm$
• B. $L=150cm,r=0.3mm$
• C. $L=250cm,r=0.1mm$
• D. $L=400cm,r=0.2mm$

Answer 1

Answer: (C)

(Young's modulus, $Y=\frac{FL}{A\Delta L}=\frac{TL}{\pi r^2\Delta L}$
$\Rightarrow \Delta L=\frac{TL}{\pi r^{2}Y}$
As wires are of same material,
so $Y$ is same for all.
Also $T$ is same,
so $\Delta L\propto \frac{L}{r^2}$.
Thus, $\frac{L}{r^2}$ is maximum for length,
$L=250cm$ and radius, $r=0.1mm$,
i.e. $25\times 10^{7}m$,
so its extension is largest.