A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio $(l / r)$ of $105$, where $l$ is the bar length and $r$ is the radius of gyration. The coefficient of thermal expansion of steel is $12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$. Consider the effective length of the steel bar as $0.5 l$ and neglect the self-weight of the bar.
The differential increase in temperature (rounded off to the nearest integer) at which the bar buckles is
- $298^{\circ} \mathrm{C}$
- $85^{\circ} \mathrm{C}$
- $400^{\circ} \mathrm{C}$
- $250^{\circ} \mathrm{C}$