if the earth is treated as a sphere of radius Radn mass M, Its angular momentum about the axis of its rotation with period T, is

Options

A. `(MR^(2)T)/(2pi)`
B. `(4piMR^(2))/(5T)`
C. `(piMR^(2))/(T)`
D. `(2piMR^(2))/(T)`

Answer

B

Explanation

The moment of inertia I of a solid sphere about the axis of rotation through the centre is
`I=(2)/(5)MR^(2)`
`therefore ` Angular momentum `L=Iomega=(2)/(5)MR^(2)xx(2pi)/(T)`
`=(4piMR^(2))/(5T)` where T=time period of rotation.