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Q.
If the spinning speed of the earth is increased then weight of the body at the equator:
AFMCAFMC 2002
Solution:
Equatorial radius is nearly $21\, km$ larger then the polar radius of earth.
Earth is rotating about its own axis with an angular velocity $\omega$. As a result of this rotation, all bodies on earth move along circular paths with same angular velocity $\omega$. Also it will have centripetal acceleration $r \omega^{2}$ directed towards its center. This acceleration is provided by acceleration due to gravity $g$.
Therefore, effective value of acceleration due to gravity is decreased. Let it be $g'$, then .
At the equator, the value of $r$ is maximum. As we go polewards $r$ goes on decreasing and becomes zero exactly at the poles. Therefore, centripetal acceleration is maximum at equator and goes on decreasing polewards.
Hence, at equator
$g'=g-R_{e} \omega^{2}$ (minimum)
If there is an increase in the angular velocity of earth, then the weight of bodies will decrease at all places.
