A rectangular loop has mass M and sides a and b. An axis ${\mathrm{OO}}^{\text{'}}$ passes tlrrough the centre C of the loop and is parallel to side a (lie in the plane of the loop). Then the radius of gyration of the loop, for the axis ${\mathrm{OO}}^{\text{'}}$ is

• A

  $\frac{\mathrm{b}}{2}\sqrt{\frac{\mathrm{b}+3\mathrm{a}}{3(\mathrm{b}+\mathrm{a})}}$

• B

  $\sqrt{\frac{({\mathrm{a}}^2+{\mathrm{b}}^2)}{12}}$

• C

  $\sqrt{\frac{{\mathrm{b}}^2+3{\mathrm{a}}^2}{12}}$

• D

  none of these