The potential energy of interaction between the semicircular ring of mass M and radius R, and the particle of mass M placed at the centre of curvature of the semicircular arc is

• A

  $-\frac{{\mathrm{GM}}^2}{\mathrm{R}}$

• B

  $-\frac{2{\mathrm{GM}}^2}{\mathrm{R}}$

• C

  $-\frac{{\mathrm{GM}}^2}{\mathrm{\pi R}}$

• D

  none of these