The speed of a transverse wave passing through a string of length \(50 \;cm\) and mass \(10\,g\) is \(60\,ms ^{-1}\). The area of cross-section of the wire is \(2.0\,mm ^{2}\) and its Young's modulus is \(1.2 \times 10^{11}\,Nm ^{-2}\). The extension of the wire over its natural length due to its tension will be \(x \times 10^{-5}\; m\). The value of \(x\) is \(...\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.