One end of a steel wire of radius ' \(r\) ' is fixed to a ceiling and a load of \(3 \mathrm{~kg}\) is attached to the free end of the wire. Another wire made of copper of radius ' \(2 r\) ' is attached to the bottom of \(3 \mathrm{~kg}\) load and a \(2 \mathrm{~kg}\) load is attached to the free end of the copper wire. The ratio of longitudinal strains produced in copper and steel wires is
(Young modulus of steel \(=20 \times 10^{10} \mathrm{Nm}^{-2}\) )
(Young modulus of copper \(=12 \times 10^{10} \mathrm{Nm}^{-2}\) )

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.