Q156 / 160 · WBJEE 2012 · Physics
Let $L$ be the length and d be the diameter of cross-section of a wire. Wires of the same material with different $L$ and $d$ are subjected to the same tension along the length of the wire. In which of the following cases, the extension of wire will be the maximum?
- A$L=200 \mathrm{cm}, \mathrm{d}=0.5 \mathrm{mm}$
- B$L=300 \mathrm{cm}, \mathrm{d}=1.0 \mathrm{mm}$
- Correct answerC$L=50 \mathrm{cm}, \quad d=0.05 \mathrm{mm}$
- D$L=100 \mathrm{cm}, \mathrm{d}=0.2 \mathrm{mm}$
Solution
We know
$$
\Delta l=\frac{F \times l}{A \times Y}=\frac{4 L}{\pi d^{2}}
$$
Here $\frac{4}{\pi}$ is a constant.
Hence, $\Delta l \propto \frac{L}{d^{2}}$
Hence, the correct answer is option: 'C'.