Question

If there were a great migration of people toward the Earth's equator, the length of the day would

(a) increase because of conservation of angular momentum.

(b) decrease because of conservation of angular momentum.

(c) decrease because of conservation of energy.

(d) increase because of conservation of energy.

(e) remain unaffected.

Short answer

The correct option is (a).

Step-by-step solution

Conservation of angular momentum

In the absence of an external torque, the angular momentum is conserved.For angular momentum conservation, if the radius of the rotational path increases, the moment of inertia increases, and the rotational speed decreases.

Explanation

When people migrate toward the Earth's equator, the distance of the people from the poles increases. i.e., their moment of inertia increases.

People are inside the Earth system; as their moment of inertia increases, the total moment of inertia of the Earth increases. Thus, according to angular momentum conservation, the angular speed of the Earth decreases.

The angular speed of the Earth decreases, which means the Earth takes more time to complete one full rotation. Therefore, the length of the day increases due to the conservation of angular momentum.