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

a. decrease because of conservation of angular momentum.
b. remain unaffected.
c. increase because of conservation of angular momentum.
d. decrease because of conservation of energy.
e. increase because of conservation of energy.

C. increase because of conservation of angular momentum.

Explanation:

We know that if there is no any external torque on the system then the angular momentum of the system will be conserved.

Angular momentum L

L = I ω

I=Mass moment of inertia ,  ω=Angular speed

If angular momentum is conserved

I₁ω₁ = I₂ω₂

If people migrates towards  Earth's equator then mass moment of inertia will increases.

I₂ > I₁

Then we can say that ω₁  > ω₂ ( angular momentum is conserve)

We know that time period T given as

If ω₂ decrease then T₂ will increase .It means that length of the day will increase.

Therefore answer is C.