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Physics Question on elastic moduli

A metal rod of length ????and cross-sectional area ????is heated through ???? ∘C???? \, {^{\circ}C}. What is the force required to prevent the expansion of the rod lengthwise ? [Y = Young's modulus of the material of rod , α\alpha = coefficient of linear expansion]

A

YAαT(1−αT)\frac{Y A \alpha T}{(1 - \alpha T)}

B

YAαT(1+αT)\frac{Y A \alpha T}{(1 + \alpha T)}

C

(1−αT)YAαT\frac{(1 - \alpha T)}{Y A \alpha T}

D

(1+αT)YAαT\frac{(1 + \alpha T)}{Y A \alpha T}

Answer

YAαT(1+αT)\frac{Y A \alpha T}{(1 + \alpha T)}

Explanation

Solution

Answer (b) YAαT(1+αT)\frac{Y A \alpha T}{(1 + \alpha T)}