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(B) When the temperature of the rod increases by $\Delta t$,it tends to expand by an amount $\Delta L = L \alpha \Delta t$.Since the rod is clamped be

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$Y A \alpha \Delta t$

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(B) When the temperature of the rod increases by $\Delta t$,it tends to expand by an amount $\Delta L = L \alpha \Delta t$.Since the rod is clamped between two rigid supports,this expansion is prevented,resulting in a compressive strain $e = \frac{\Delta L}{L} = \alpha \Delta t$.According to Hooke's Law,the stress $\sigma$ is given by $\sigma = Y e$,where $Y$ is the Young's modulus.Substituting the strain,we get $\sigma = Y \alpha \Delta t$.Since stress is defined as force per unit area $(\sigma = \frac{F}{A})$,the force $F$ exerted on the supports is $F = \sigma A$.Therefore,$F = Y A \alpha \Delta t$.

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