Three particles, each of mass M are moving in a circle under their mutual gravitational forces such that they always form an equilateral triangle of side a while rotating. time period of motion of any particle is :

• A

  $2\mathrm{\pi }\sqrt{\frac{{\mathrm{a}}^2}{\mathrm{GM}}}$

• B

  $2\mathrm{\pi }\sqrt{\frac{{\mathrm{a}}^3}{3\mathrm{GM}}}$

• C

  $2\mathrm{\pi }\sqrt{\frac{{\mathrm{a}}^2}{5\mathrm{GM}}}$

• D

  $2\mathrm{\pi }\sqrt{\frac{{\mathrm{a}}^3}{5\mathrm{GM}}}$