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).
