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A circular metallic rod of length $250 \: mm$ is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of $0.2 \: mm$ between the rod and the wall on the right side. If the temperature of the rod is increased by $200^\circ  C$, the axial stress developed in the rod is __________ $MPa$.
Young’s modulus of the material of the rod is $200 \: GPa$ and the coefficient of thermal expansion is $10^{−5}$ per $_{}^{\circ}\textrm{C}$.

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