Question

Due to global warming, if the ice in the polar region melts and some of this water flows to the equatorial region, then

• A. Angular momentum of the earth increases and duration of day increases
• B. Angular momentum of the earth decreases and duration of day decreases
• C. Angular momentum of the earth is constant and duration of day decreases
• D. Angular momentum of the earth is constant and duration of day increases

Hint:

$L = I\omega$. If mass redistributes away from the axis, $I$ goes up, $\omega$ goes down, and Time Period ($T$) goes up (rotation slows down).

Answer 1

The Correct Option is D

Step 1: Conservation of Angular Momentum:
Since there is no external torque acting on the Earth, its angular momentum ($L$) remains constant. \[ L = I\omega = \text{constant} \]
Step 2: Change in Moment of Inertia ($I$):
Water flows from the poles (distance from axis $r \approx 0$) to the equator (distance from axis $r = R$). Since mass is moving to a larger distance from the axis of rotation, the moment of inertia $I = \sum mr^2$ increases.
Step 3: Effect on Time Period:
Since $L = I\omega$ is constant and $I$ increases, the angular velocity $\omega$ must decrease. The duration of the day is $T = \frac{2\pi}{\omega}$. As $\omega$ decreases, $T$ increases. Conclusion:
Angular momentum is constant, and the duration of the day increases.