Question

a meteor is falling towards the earth. If the mass and radius of the earth are 6×10^24 kg and 6.4×10^6 m respectively. Find the hieght of the meteor where its acceleration due to gravity is 4m/s^2​

Answer 1

Answer:

3.6×10⁶ m

Explanation:

Newton's law of universal gravitation states that the force between two masses is:

F = GMm / r²

where G is the universal constant of gravitation (6.67×10⁻¹¹ m³/kg/s²),

M is the mass of one object

m is the mass of the other object,

and r is the distance between the center of masses of the objects.

The force acting on the meteor is:

∑F = ma

GMm / r² = ma

GM / r² = a

Given M = 6×10²⁴ kg and a = 4 m/s²:

(6.67×10⁻¹¹ m³/kg/s²) (6×10²⁴ kg) / r² = 4 m/s²

r = 10⁷ m

The distance from the meteor to the center of the Earth is 10⁷ m.  We want to know what the height of the meteor is (distance to the surface of the Earth).  So we need to subtract the Earth's radius.

h = 10⁷ m − 6.4×10⁶ m

h = 3.6×10⁶ m