Q128 / 180 · KCET 2011 · Physics
The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension, when the same tension is applied?
- Correct answerA$L=100 \mathrm{~cm}, r=0.2 \mathrm{~mm}$
- B$L=200 \mathrm{~cm}, r=0.4 \mathrm{~mm}$
- C$L=300 \mathrm{~cm}, r=0.6 \mathrm{~mm}$
- D$L=400 \mathrm{~cm}, r=0.8 \mathrm{~mm}$
Solution
Extension of wire $e=\frac{F L}{A Y}$
$$
e=\frac{F L}{\pi r^{2} Y}
$$
$F$ and $Y$ are same for all wires
$\therefore$
$$
\begin{aligned}
&e \propto \frac{L}{r^{2}} \\
&e_{a}=\frac{1000}{0.2 \times 0.2}=25000 \\
&e_{b}=\frac{2000}{0.4 \times 0.4}=12500 \\
&e_{c}=\frac{3000}{0.6 \times 0.6}=8333.4 \\
&e_{d}=\frac{4000}{0.8 \times 0.8}=6250
\end{aligned}
$$
We can see that, first wire have the largest extension.
Hence, the correct answer is option: 'A'.