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(D) The effective acceleration due to gravity $g'$ at a latitude $\phi$ is given by the formula: $g' = g - \omega^2 R \cos^2 \phi$,where $\omega$ is t

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

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(D) The effective acceleration due to gravity $g'$ at a latitude $\phi$ is given by the formula: $g' = g - \omega^2 R \cos^2 \phi$,where $\omega$ is the angular velocity of the earth and $R$ is the radius of the earth.At the poles,the latitude $\phi = 90^\circ$,so $\cos 90^\circ = 0$. Thus,$g' = g$,which means there is no change in gravity at the poles regardless of the change in $\omega$.At all other latitudes,as the angular velocity $\omega$ increases,the term $\omega^2 R \cos^2 \phi$ increases.Since $g' = g - \omega^2 R \cos^2 \phi$,an increase in $\omega$ leads to a decrease in $g'$.Consequently,the weight of an object,$W = mg'$,will decrease at all points on the earth except at the poles.

Suppose that the angular velocity of rotation of the earth is increased. Then,as a consequence:

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