When the temperature  of a rod increases from t to $\mathrm{t}+\mathrm{\Delta t}$ , its moment of inertia increases from I to $\mathrm{I}+\mathrm{\Delta I}$ . If    be the coefficient of linear expansion of the rod, then the value of  $\frac{\mathrm{\Delta I}}{\mathrm{I}}$ is

• A

  $2\mathrm{\alpha \Delta t}$

• B

  $\mathrm{\alpha \Delta t}$

• C

  $\frac{\mathrm{\alpha \Delta t}}{2}$

• D

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