If the speed of rotation of the Earth about its own axis increases, what happens to the apparent weight of a body at the equator?

Introduction / Context:
The Earth rotates about its axis, and this rotation influences the apparent weight of objects on the surface. Weight as measured by a scale is the normal reaction exerted by the surface, which can differ from the gravitational force because of rotational effects. This question asks what happens to the apparent weight at the equator if the rotational speed increases, illustrating the role of centripetal acceleration in everyday physics.

Given Data / Assumptions:

• The Earth is rotating about its axis with some angular speed.
• A body is located at the equator where the rotational speed relative to the axis is maximum.
• Gravitational force acting on the body is approximately constant and directed toward the centre of the Earth.
• The body moves in a circular path due to Earth rotation, so it requires centripetal acceleration toward the axis.
• We ignore small variations in gravitational field due to shape and density changes.

Concept / Approach:
The true gravitational force on the body pulls it toward the centre. However, because the body is in circular motion with the rotating Earth, a centripetal force is needed and is provided by part of the gravitational force. The remaining part appears as the normal reaction that we interpret as apparent weight. As the angular speed increases, the required centripetal force increases and a larger fraction of gravity is used for centripetal acceleration. Consequently, the normal reaction, and thus the apparent weight, decreases. At the equator this effect is strongest, but normal rotation rates are far from sufficient to make the weight exactly zero.

Step-by-Step Solution:
Step 1: Let the gravitational force on the body be Fg, directed toward the centre of the Earth.Step 2: For circular motion at the equator with angular speed omega, the required centripetal force is Fc = m * omega^2 * R, where R is the radius of the Earth.Step 3: The normal reaction N from the ground satisfies Fg minus N = Fc, so N = Fg minus m * omega^2 * R.Step 4: As omega increases, the term m * omega^2 * R becomes larger, so N decreases, meaning the apparent weight measured on a scale becomes smaller.

Verification / Alternative check:
If the Earth did not rotate at all, the centripetal term would be zero and apparent weight would equal the full gravitational force. In reality, measured weight at the equator is slightly less than at the poles, consistent with existing rotation. In a thought experiment where the rotation becomes extremely fast, there would be a critical speed at which m * omega^2 * R equals Fg, making N equal zero and giving weightlessness at the equator. This confirms that increasing rotation speed always reduces apparent weight before any such extreme condition is reached.

Why Other Options Are Wrong:
Option a is wrong because an increase in centripetal requirement means that more of gravity is used for circular motion, leaving less for the normal reaction, so apparent weight decreases rather than increases. Option c is incorrect since experimental measurements already show weight differences between equator and poles due to rotation and shape. Option d is not correct for arbitrary nonzero rotation; weight becomes zero only at a very high critical speed, not at any small increase. Option e has no physical basis, as daily cycles do not change the rotation speed of the Earth in this manner.

Common Pitfalls:
Students may confuse centripetal force with a separate physical force rather than seeing it as the net inward force required for circular motion. Another common error is to assume that gravity alone always equals weight, ignoring situations like lifts, roller coasters, or rotating frames where apparent weight changes. Remember that weight in the practical sense is the normal reaction, and any effect that changes this reaction, such as increased rotation speed, will change the measured weight on a scale.

Final Answer:
Its apparent weight decreases because the outward centripetal effect reduces the normal reaction.