Acceleration due to gravity on moon is 1/6 of the acceleration due to gravity on earth. If the ratio of densities pf earth $\left({\mathrm{\rho }}_{\mathrm{e}}\right)$ and moon $\left({\mathrm{\rho }}_{\mathrm{m}}\right)$ is $\left(\frac{{\mathrm{\rho }}_{\mathrm{e}}}{{\mathrm{\rho }}_{\mathrm{m}}}\right)=\frac{5}{3}$ then radius of moon R_m in terms of R_e will be

• A

  $\frac{5}{18}{\mathrm{R}}_{\mathrm{e}}$

• B

  $\frac{1}{6}{\mathrm{R}}_{\mathrm{e}}$

• C

  $\frac{7}{18}{\mathrm{R}}_{\mathrm{e}}$

• D

  $\frac{1}{2\sqrt{3}}{\mathrm{R}}_{\mathrm{e}}$