The following four wires are made of the same material. Which of these will have the largest extension when…

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?
  1. Length $=50 \mathrm{~cm}$, diameter $=0.5 \mathrm{~mm}$
  2. Length $=100 \mathrm{~cm}$, diameter $=1 \mathrm{~mm}$
  3. Length $=200 \mathrm{~cm}$, diameter $=2 \mathrm{~mm}$
  4. Length $=300 \mathrm{~cm}$, diameter $=3 \mathrm{~mm}$

Solution

$\Delta L=\frac{F L}{A Y}$
or $\Delta L \propto \frac{L}{d^2} \quad\left[\because A=\frac{\pi d^2}{4}\right]$
Therefore, $\Delta$ will be maximum for that wire which $\frac{L}{A}$ is maximum, so option (1) is correct. ~

Asked in: NEET 2013 (All India)

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