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The acceleration due to gravity at the p...

The acceleration due to gravity at 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

A

`(omega^(2))/(R_(E))`

B

`(omega^(2))/(R_(E)^(2))`

C

`omega^(2)R_(E)^(2)`

D

`omega^(2)R_(E)`

Text Solution

Verified by Experts

The correct Answer is:
D
(d) Acceleration due to gravity at a place of lattitude `lambda` due to the rotation of earth is
`g'=g-R_(E)omega^(2)cos^(2)lambda`
At equator ,` lambda=0^(@), cos90^(@)=0`
`:.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)`
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