Question

If the rotational speed of earth is increased then weight of a body at the equator:
A) Increases
B) Decreases
C) Becomes double
D) Does not change

Answer 1

Hint: We know that the weight of a body depends on the gravitational force and other forces acting on the body. For this question, as the rotational speed of Earth is changed, the value of acceleration due to gravity will change. Recall, when we are in lift, we feel heavier and lighter when lift is moving upwards and downwards respectively.

Complete step by step solution:
Let us first look at option C, with increase in rotational speed of Earth the weight of a body becomes double. Clearly this option can be safely eliminated. Let’s see how:
As per option C, the weight increases and becomes double which means with increase in rotational speed of Earth, the weight of the body will increase. But if we observe carefully, the weight is doubled and if the rotational speed further increases then there is no change in weight of a body. Therefore, we can eliminate this option.

When the Earth rotates or for any rotating body, centrifugal force acts towards the center of the rotation. Since, the body is intact, that is there must be an equal force acting in the opposite direction. This force is called the centrifugal force. The direction of centrifugal force is opposite to the direction of centripetal force. Centrifugal force is pseudo force, it does not exist as there is no gravity, electrical force or magnetic force to bring about this force.
As the weight of a body $ = m \times g$ .
Where \[m\] is the mass of the body
$g$ is the acceleration due to gravity.
Then under the effect of increased rotation,
Weight of body will be $ = mg' = mg - $ Centrifugal force
Where $g'$ is the decreased acceleration due to gravity.
For rotating, the centrifugal acceleration \[ = R{\omega ^2}{\cos ^2}\theta \] where $R$ is the radius, \[\omega \] is the angular velocity and \[\theta \] is the angle with the equator which is zero in this case.
As we can clearly see from the formula, as the angular speed increases the net acceleration due to gravity will decrease. As a result, the weight will decrease.

Therefore, option (B) is the correct option.

Note: Remember that the angle of a body on the surface is taken with respect to the equator. Also be careful when interpreting the result, as angular speed increases the weight will decrease. Also remember that centrifugal force is pseudo force (imaginary force) while centripetal force is a real force.