$A$ metal rod of length $L$ and cross-sectional area $A$ is heated through $T^{\circ} C$. What is the force required to prevent the expansion of the rod lengthwise? ($Y=$ Young's modulus of the material of the rod,$\alpha=$ coefficient of linear expansion of the rod.)

• A
  $YA \alpha / T(1+\alpha T)$
• B
  $YA \alpha T /(1-\alpha T)$
• C
  $YA \alpha T /(1+\alpha T)$
• D
  $YA \alpha /(1-\alpha T)$