$A$ metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L$, $\alpha$, and $Y$ denote the length of the rod, the coefficient of linear thermal expansion, and the Young's modulus of its material respectively, then for an increase in temperature of the rod by $\Delta T$, the longitudinal stress developed in the rod is
- Ainversely proportional to $\alpha$
- Binversely proportional to $Y$
- Cdirectly proportional to $\Delta T$
- Dindependent of $L$
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