Respuesta :
m = mass of the person = 80 kg
M = mass of earth = 5.98 x 10²⁴ kg
R = radius of earth = 6.37 x 10⁶ m
h = height above the earth's surface = 1400 km = 1.4 x 10⁶ m
r₁ = initial distance of the person from the center of earth when on surface = R = 6.37 x 10⁶ m
r₂ = final distance of the person from the center of earth when at some height = R + h = 6.37 x 10⁶ + 1.4 x 10⁶ = 7.77 x 10⁶ m
F₁ = Gravitational force of earth on the person when at surface
Gravitational force of earth on the person when at surface is given as
F₁ = G M m/r₁² eq-1
F₂ = Gravitational force of earth on the person when at some height
Gravitational force of earth on the person when at some height is given as
F₂ = G M m/r₂² eq-2
dividing eq-1 by eq-2
F₁ /F₂ = (G M m/r₁² )/(G M m/r₂²)
F₁ /F₂ = r₂²/r₁²
inserting the values
F₁ /F₂ = (7.77 x 10⁶)²/(6.37 x 10⁶)²
F₁ /F₂ = 1.49
The required ratio of Earth's gravitational force at Earth's surface and at a given height is 1.49.
What is Gravitational Force?
The force of attraction between all the massive particles and giant bodies is known as gravitational force. This is also known as the Universal Force of attraction.
Given data:
The mass of person is, m = 80 kg.
The mass of Earth is, M = 5.98 x 10²⁴ kg.
The radius of Earth is, r = 6.37 x 10⁶ m.
The height above the Earth's surface is, h = 1400 km = 1.4 x 10⁶ m.
Now, let us calculate the total distance above the surface of Earth. Then,
r' = R + h
r' = 6.37 x 10⁶ + 1.4 x 10⁶
r' = 7.77 x 10⁶ m
Let,
F₁ = Gravitational force of Earth on the person when at the surface.
F₂ = Gravitational force of Earth on the person when at some height.
Then, the expression for the gravitational force of Earth on the person when at surface is given as,
F₁ = G M m/r² ..................................................................(1)
here,
G is the universal gravitational constant.
And the expression for the Gravitational force of Earth on the person when at some height is given as,
F₂ = G M m/r'² ..................................................................(2)
Taking ratio of eq. (1) and (2) as,
F₁ /F₂ = (G M m/r² )/(G M m/r'²)
F₁ /F₂ = r'²/r²
F₁ /F₂ = (7.77 x 10⁶)²/(6.37 x 10⁶)²
F₁ /F₂ = 1.49
Thus, we can conclude that the required ratio of Earth's gravitational force at Earth's surface and at a given height is 1.49.
Learn more about the gravitational force here:
https://brainly.com/question/21500344
