Acceleration due to gravity at the pole of earth is g, at the equator it is $\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$n$}\right.(n>1)$. If R be the ratios of earth then time period of spin of earth is 

• A

  $2\pi \sqrt{\frac{Rn}{g}}$

• B

  $2\pi \sqrt{\frac{Rn}{g(n-1)}}$

• C

  $2\pi \sqrt{\frac{R}{g(n-1)}}$

• D

  $2\pi \sqrt{\frac{Rn}{g(n+1)}}$