The acceleration due to gravity g and density of the pols and the equator is `g_(p) and g_(e)` respectively. If the earth is a sphere of radius `R_(E)` and rotating about its axis with angular speed `omega and g_(p)-g_(e)` given by

Options

A. `(omega^(2))/(R_(E))`
B. `(omega^(2))/(R_(E)^(2))`
C. `omega^(2)R_(E)^(2)`
D. `omega^(2)R_(E)`

Answer

D

Explanation

Acceleration due to gravity at a place of latitude `lambda` due to the rotation of earth is
`g'=g-R_(E)omega^(2)cos^(2)lambda`
At equator, `lambda =0^(@), cos0^(@)=1`
`:. g'=g_(e)=g- R_(E)omega^(2)`
At poles, `lambda=90^(@), cos90^(@)=0`
`:. g'=g_(P)=g`
`:. g_(P)-g_(e)=g-(g-R_(E)omega^(2))=R_(E)omega^(2)`