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A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion $α$/°C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $∆$T K. Young's modulus, Y, for this metal is :

(1) $F\over2A\alpha\Delta T$

(2) $F\over A\alpha(\Delta T-273)$

(3) $F\over A\alpha\Delta T$

(4) $2F\over A\alpha\Delta T$
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Ans: (3) $F\over A\alpha\Delta T$

Sol: Young's modulus $y = {Stress\over Strain}$

$={F / A \over (\Delta l / l)}$

$={F\over A\alpha\Delta T}$

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