What is the moment of inertia of earth about its diameter. Taking it to be a sphere of radius 6400 km and mass `6 xx 10 ^(24) kg`

Options

A. `11. 6 xx 10 ^(24) kg m ^(2)`
B. ` 6 xx 10 ^(34) kg m ^(2)`
C. `9. 83 xx 10 ^(37) kg m ^(2)`
D. None of these

Explanation

To find the moment of inertia of the Earth about its diameter, we can use the formula for the moment of inertia of a solid sphere, which is given by:

\[ I = \frac{2}{5} m r^2 \]

where:
- \( I \) is the moment of inertia,
- \( m \) is the mass of the sphere,
- \( r \) is the radius of the sphere.
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