If the earth is treated as a sphere of radius R and mass m its angular momentum about the axis of its rotation with period T is

Explanation

Here's how to find the angular momentum of the Earth treated as a sphere:1. Moment of inertia:The first step is to determine the moment of inertia (I) of the Earth. For a uniform sphere, the moment of inertia about an axis passing through its center is:I = (2/5) * MR^2where:M is the mass of the EarthR is the radius of the Earth2. Angular velocity:The angular velocity (ω) is related to the period (T) by the following equation:ω = 2π / Twhere:T is the period of rotation (1 day in this case)3. Angular momentum:Finally, the angular momentum (L) of the Earth is the product of its moment of inertia and angular velocity:L = I * ωCombining the equations:Substitute the expressions for I and ω:L = ((2/5) * MR^2) * (2π / T)Simplify:L = (4π * MR^2) / (5T)Therefore, the angular momentum of the Earth about the axis of its rotation with period T is (4π * MR^2) / (5T).