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

• A

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

• B

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

• C

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

• D

  $\mathrm{Y} \mathrm{\alpha } {\mathrm{t}}^2$