Question

Moment of inertia of earth about its axis of rotation is ____________.

Options

• `2/3 pi "R"^5 rho`

• `2/5 pi "R"^5 rho`

• `8/15 pi "R"^5 rho`

• `4/15 pi "R"^5 rho`

Answer 1

Moment of inertia of earth about its axis of rotation is `8/15 pi "R"^5 rho`.

Explanation:

`"Earth is solid sphere, so"  "M.I" = 2/5 "MR"^2`

`"where", "M" = 4/3 pi "R"^3 rho`

`therefore "M.I" = 2/5 [4/3 pi "R"^3 rho] "R"^2`

`= 8/15 pi "R"^5 rho`