Question

a meteor 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.
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Answer 1

Answer:

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,

                                      $g_{h}$ = GM/$R_{h}^{2}$

Where,

                                     $R_{h}^{2}$ = R + h

                                 $R_{h}^{2}$ = GM/$g_{h}$

                               $R_{h}^{2}$ = 6.673 x 10⁻¹¹ X 6 x 10²⁴ / 4

                                                              = 1.00095 x 10¹⁴

                                     $R_{h}$ = 10004748.87 m

                                                              = 10004.749 km

From above,

                                     $R_{h}$ = R + h

                                      h = $R_{h}$ - 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