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A. There will be no change in weight anywhere on the earth

B. Weight of the object, everywhere on the earth, will decrease

C. Weight of the object, everywhere on the earth, will increase

D. Except at poles. weight of the object on the earth will decrease

Answer

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Let us assume a test mass m. the force of gravity acting on it is given as mg. The centrifugal force on this test charge is $m{\omega ^2}r$.As both these forces are co-initial as well as coplanar forces, we can add them vectors using parallelogram law of vector addition to get the magnitude of the apparent value of the gravitational force as,

${\left( {mg'} \right)^2} = {\left( {mg} \right)^2} + {\left( {m{\omega ^2}r} \right)^2} + 2(mg)(m{\omega ^2}r)\cos (\pi - \theta )$

Where r is the radius of the circular path and ‘R’ is the radius of the earth, then $r = R\cos \theta $.

Substituting the value of r we get,

$g' = g - R{\omega ^2}\cos (2\theta )$

Where g′ is the apparent value of acceleration due to gravity at the latitude due to the rotation of the earth and g is the true value of gravity at the latitude without considering the rotation of the earth.

At poles, $\theta = 90^\circ \Rightarrow g' = g$.

At the equator,$\theta = 0^\circ \Rightarrow g' = g - {\omega ^2}R$ .