A metal rod of length $L$ and cross-sectional area $A$ is heated through $T °\mathrm{C}$. What is the force required to prevent the expansion of the rod lengthwise?

$[Y$ = Young's modulus of the material of rod, $\alpha =$ coefficient of linear expansion$]$

• A

  $\frac{YA\alpha T}{(1-\alpha T)}$
• Correct answer
  B

  $\frac{YA\alpha T}{(1+\alpha T)}$
• C

  $\frac{(1-\alpha T)}{YA\alpha T}$
• D

  $\frac{(1+\alpha T)}{YA\alpha T}$

Hence, the correct answer is option: 'B'.