Question

If the spinning speed of the earth is increased then weight of the body at the equator:

• A. does not change
• B. doubles
• C. decreases
• D. increases

Answer 1

Answer: (C)

Equatorial radius is nearly $21km$ 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 $g^{\prime }$, 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
$g^{\prime }=g-R_e{\omega }^2$ (minimum)
If there is an increase in the angular velocity of earth, then the weight of bodies will decrease at all places.