Ameteor is falling towards the earth. if the mass and the radius of the earth are 6×10^24kg and 6.4×10^3km respectively, find the height of the meteor from the earths's surface where its acceleration due to gravity becomes 4m/s^2.
answer=3600km

h = 3600 km

Explanation:

Given,

The mass of the Earth, M = 6 x 10²⁴ km

The radius of the Earth, R = 6.4 x 10³ km

The acceleration of the meteor at height, x = 4 m/s²

The acceleration due to gravity at the surface of the Earth is given by the formula,

                                    g = GM/R²

At height 'h' acceleration is given by the formula,

                                     gₓ = GM/Rₓ²

                                    Rₓ² =  GM/gₓ

                                          = 6.673 x 10⁻¹¹ X 6 x 10²⁴ / 4

                                          = 1 x 10¹⁴

                                       Rₓ = 1 x 10⁷ m

Where,

                                  Rₓ = R + x

                                   x = Rₓ - R

                                        = 10000 km - 6400 km

                                        = 3600 km

Hence, the height of the meteor where its acceleration due to gravity is 4 m/s² is, h = 3600 km

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