Three uniform thin aluminium rods each of length \(2 \mathrm{~m}\) form an equilateral triangle \(P Q R\) as shown in the figure. The mid point of the \(\operatorname{rod} P Q\) is at the origin of the coordinate system. If the temperature of the system of rods increases by \(50^{\circ} \mathrm{C}\), the increase in \(y\)-coordinate of the centre of mass of the system of the rods is ............ \(\mathrm{mm}\). (Coefficient of volume expansion of aluminium \(=12 \sqrt{3} \times 10^{-6} \mathrm{~K}^{-1}\) )

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.