If earth is supposed to be sphere of radius R, if `g_(20)` is value of acceleration due to gravity at latitude of `30^(@)` and g at the equator, then value of `g-g_(30^(@))` is

Options

A. `(1)/(4)omega^(2)R`
B. `(3)/(4) omega^(2)R`
C. `omega^(2)R`
D. `(1)/(2) omega^(2)R`

Answer

B

Explanation

Acceleration due to gravity at latitude `phi` is given by
`g'=g-Romega^(2)cos^(2)phi`
At `30^(@),g_(30^(@))=g-R omega^(2)cos^(2)30^(@)=g-(3)/(4)R omega^(2)`
`:. g-g_(30^(@))=(3)/(4)omega^(2)R`.