Answer: [tex]9.72(10)^{37} kgm^{2}[/tex]
Explanation:
Assuming that the Earth is a solid sphere, of mass [tex]M[/tex] and radius [tex]R[/tex] around an axis that passes through its center, with uniform density (that is: its center of mass coincides with the center of the sphere), its moment of inertia [tex]I[/tex] is given by the following formula:
[tex]I=\frac{2}{5}MR^{2}[/tex] (1)
Where:
[tex]M=5.97(10)^{24}kg[/tex]
[tex]R=6.38(10)^{6}m[/tex]
[tex]I=\frac{2}{5}(5.97(10)^{24}kg)(6.38(10)^{6}m)^{2}[/tex] (2)
Finally:
[tex]I=9.72(10)^{37}kg.m^{2}[/tex]
