A uniform metal bar of length \(10 \mathrm{~m}\) with a crack at its midpoint is clamped between two rigid supports. The bar buckles upward due to temperature rise of \(40^{\circ} \mathrm{C}\). If the coefficient of linear expansion of the metal is \(2.5 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}\), the maximum displacement of the mid-point of the bar 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.