Question

The masses of the Moon and Earth are 7.35 x 1022 kg and 5.97 x 1024 kg, respectively. The strength of the gravitational force between them is 1.98 x 1020 N. What is distance between the centre of the Earth and the centre of the Moon?

Answer 1

Distance between centre of Earth and centre of Moon is 3.85 x 10⁸ m

Step-by-step explanation:

The attractive force experienced by two mass objects is known as Gravitational force.

The gravitational force is determine by the relation:

`F=(Gm_(1) m_(2) )/(d^(2) )` ....(1)

According to the problem,

Mass of Moon, m₁ = 7.35 x 10²² kg

Mass of Earth, m₂ = 5.97 x 10²⁴ kg

Gravitational force experienced by them, F = 1.98 x 10²⁰ N

Universal gravitational constant, G = 6.67 x 10⁻¹¹ Nm²kg⁻²

Substitute these values in equation (1).

`1.98*10^(20) =(6.67*10^(-11)*7.35*10^(22)*5.97*10^(24) )/(d^(2) )`

`d^(2)=(2.93*10^(37))/(1.98*10^(20))`

`d=\sqrt{1.48*10^(17)}`

d = 3.85 x 10⁸ m