Ameteor is falling towards the earth. if the mass and radius of the earth are 6×10^24 kg and 6.4×10^3 km respectively. find the hieght of the meteor where its acceleration due to gravity is 4m/s^2.

h = 4004.349 km

Explanation:

Given,

The mass of the Earth, M = 6 x 10²⁷ km

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

At what height the acceleration of the meteor is, h = 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,

                                      = GM/

Where,

                                      = R + h

                                  = GM/

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

                                                              = 1.00095 x 10¹⁴

                                      = 10004748.87 m

                                                              = 10004.749 km

From above,

                                      = R + h

                                      h = - R

                                         = 10004.749 km - 6400 km

                                         = 4004.349 km

Hence, the hieght of the meteor where its acceleration due to gravity is 4 m/s² is, h = 4004.349 km