Question

State How Acceleration due to gravity g varies with
i. Shape of the earth
ii. height from the earth surface
iii. depth from the earth surface
iv. latitude of a particular place on the earth.

Answer 1

Answer:

i) Acceleration due to gravity at the pole is greater than that at the equator, this is because the shape of the earth is elliptical, as a result, the radius at the equator is greater than at the pole, and the value of g is inversely proportional to the radius, hence it increases at the pole.

ii) The value of g decreases with increasing altitude. It is given by -:

g2 = g1/(1 + h/Re)^2

iii) As we go below the earth's surface, the value of g decreases. It is max. at the surface of the earth and decreases as we move above or below it. At a certain depth h, the value of g is given by -:

g2 = g1(1 - h/Re)

iv) The latitude at a certain point on the earth also make the value of g vary. The latitude is the angle between the equatorial plane and the line joining that point to the centre of the earth. So when the latitude is 0°, (at the equator) value of g decreases. When the latitude Is 90°(at the pole), value of g increases. It is given by -:

g2 = g1 - Re × omega^2 × cos^2 theta

Key to variables -:

1) g2 = the value of acc. due to gravity at that certain point, I.e, above or below the earth's surface.

2) g1 = value of g at the surface of earth.

3) omega = angular velocity of the rotating earth.

4) theta = angle between the equatorial plane and the line joining that point to the centre of the earth, I.e, the latitude.