The Young's modulus of a steel wire of length \(6\,m\) and cross-sectional area \(3\,mm ^2\), is \(2 \times 11^{11}\,N / m ^2\). The wire is suspended from its support on a given planet. A block of mass \(4\,kg\) is attached to the free end of the wire. The acceleration due to gravity on the planet is \(\frac{1}{4}\) of its value on the earth. The elongation of wire is  (Take \(g\) on the earth \(=10\) \(\left.m / s ^2\right):\)

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.