A metal rod of Young’s modulus Y and coefficient of thermal expansion a is held at its two ends such that its length remains invariant. If its temperature is raised by ${\mathrm{t}}^0\mathrm{C},$  the linear stress developed in it is

• A

  $\frac{\mathrm{Y}}{\mathrm{\alpha t}}$

• B

  $\mathrm{Y} \mathrm{\alpha t}$

• C

  $\frac{1}{\left(\mathrm{Y\alpha t}\right)}$

• D

  $\frac{\mathrm{\alpha t}}{\mathrm{Y}}$