Question

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

(a) ) length = 200 cm, diameter =2 mm

(b) length = 300 cm, diameter -=3 mm

(c) length = 50 cm, diameter = 0.5 mm

(d) length = 100 cm, diameter = 1

Answer 1

Explanation:
Young's modulus,
where $F$ is the force applied, $L$ is the length, $D$ is the diameter and $\Delta L$ is the extension of the wire respectively. As each wire is made up of same material therefore their Young's modulus is same fol each wire. For all the four wires. Y, $F$ (= tension) are the same.
$\therefore \quad \Delta L \propto \frac{L}{D^{2}}$
In (a) $\frac{L}{D^{2}}=\frac{200 \mathrm{~cm}}{(0.2 \mathrm{~cm})^{2}}=5 \times 10^{3} \mathrm{~cm}^{-1}$
In (b) $\frac{L}{D^{2}}=\frac{300 \mathrm{~cm}}{(0.3 \mathrm{~cm})^{2}}=3.3 \times 10^{3} \mathrm{~cm}^{-1}$
In (c) $\frac{L}{D^{2}}=\frac{50 \mathrm{~cm}}{(0.05 \mathrm{~cm})^{2}}=20 \times 10^{3} \mathrm{~cm}^{-1}$
In (d) $\frac{L}{D^{2}}=\frac{100 \mathrm{~cm}}{(0.1 \mathrm{~cm})^{2}}=10 \times 10^{3} \mathrm{~cm}^{-1}$
Hence, $\Delta \mathrm{L}$ is maximum in (c).

Answer 2

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Answer 3

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