Question #24de9

2 Answers
Aug 8, 2017

g is zero at the center
g is maximum at the poles.

Explanation:

We know the equation, F = (Gm_1m_2)/r^2, where
G = Gravitational Constant
m_1 & m_2 = Masses of 2 bodies repectively
r = The distance between the 2 bodies
F = It is the force acting on the bodies

We can rewrite the equation as F = (GMm)/R^2 with respect to Earth, where
M = Mass of the Earth
m =mass of the object on Earth
R = Distance from the center of the Earth to the object

We know that F = m/a. So substituting this value for F, the Equation becomes => m/a = (GMm)/R^2

1/a = (GMm)/(R^2m)

1/a = (GMcancelcolor(red)m)/(R^2cancelcolor(red)m)

1/a = (GM)/R^2

1 = (GMa)/R^2

R^2 = GMa

G & M are constants, That means

R^2 prop a

a prop R^2

a means acceleration due to gravity. That is a = g
That means,

g prop R^2

From this, we can understand that acceleration due to gravity (g)
is directly proportional to the distance, that means when the distance from the center of the Earth and the object increases, g also increases and when the distance from the center of the Earth and the object decreases, g also decreases.

Distance from the center of the Earth to the poles is maximum, so g is maximum at the poles. When the object is at the center of the Earth, the distance between the center of the Earth and the Object will be zero, so g will also become zero.

Gravity is maximum on poles surface of earth.

Explanation:

Gravity will be almost zero at the center of earth
The diameter of Earth is about 40 KM larger at equator than poles..gravity depend upon inverse square law.