Question

If the rotational motion of earth increases, then the weight of the body-
A) will remains same
B) will increase
C) will decrease
D) none of these

Answer 1

Hint
For this question, we know that the weight of the body in the absence of the rotating motion is mg. This mg force will act in the downward direction and this will be subjected to change if centripetal force acts too. Velocities of the body change when its distance from the axis changes.

Complete step by step answer
If the earth is not spinning, the weight of the body has been mg. the earth rotating around its polar axis will make the body under circular motion too. Suppose the object is present at an angle ϕ with the polar axis, then the distance (radius) from the axis is $R\sin \phi $. The centripetal force is given by $\dfrac{{m{v^2}}}{r}$or, if the object is at a distance r from the axis. Therefore, we may write
$mg' = mg - m{\omega ^2}R\sin \phi $
cancelling the m, we get
$g' = g - {\omega ^2}R\sin \phi $
In the question it has been asked to find what happens to the g when our object is at equator. So, we are given $\phi = {90^0}$
This clearly helps us see that the object at the equator will have g’ that is smaller than the actual g.
Therefore, the correct answer is (C), The weight of the body decreases.

Note
To clear up the formula, consider drawing two perpendicular axes at the point where the object is present. Now, see what angle the centripetal force makes with these axes. mg will be always directed towards the centre of the earth, no matter where it present and centripetal force points out from the circle that the object makes.