$A$ rod of length $L$ at room temperature and uniform area of cross section $A$ is made of a metal having a coefficient of linear expansion $\alpha /^{\circ}C$. It is observed that an external compressive force $F$,applied on each of its ends,prevents any change in the length of the rod when its temperature rises by $\Delta T \, K$. The Young's modulus $Y$ for this metal is:
- A$\frac{F}{A \alpha \Delta T}$
- B$\frac{F}{A \alpha (\Delta T - 273)}$
- C$\frac{F}{2A \alpha \Delta T}$
- D$\frac{2F}{A \alpha \Delta T}$
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