## Unit – II B |

## Effect of Shape of Earth and Latitude of a Place on Acceleration Due to Gravity:

### Variation of ‘g’ due to shape of the earth Variation of acceleration due to gravity

- We have proved that, thus

- Thus, the acceleration due to gravity at a place is inversely proportional to the square of the distance of the point from the centre of the earth.
- Now, the earth is not perfectly spherical. It is flattened at the poles and elongated on the equatorial region. The radius of the equatorial region is approximately 21 km more than that at the poles.
- Hence acceleration due to gravity is maximum at the poles and minimum at the equator.
- As we move from the equator to pole the distance of the point on the surface of the earth from the centre of the earth decreases. Hence the acceleration due to gravity increases

### Variation of ‘g’ due to the latitude of the place:

- The latitude of a point is the angle ‘’ between the equatorial plane and the line joining that point to the centre of the earth. Latitude of the equator is 0° and that of poles is 90°.
- Let us consider point P with latitude ‘Φ’ as shown on the surface of the earth. Let ‘g
_{Φ}’ be the acceleration due to gravity at point P. - Let ‘r’ be the distance of point P from the axis of the earth. Due to rotational motion of the earth about its axis the body at P experiences a centrifugal force which is given by mrω
^{2}. Let us resolve this centrifugal force into rectangular components. Its component along the radius of the earth is ‘mrω^{2}. cosΦ’.

- The effective weight of the body at P will be the difference between true weight and centrifugal force acting on the body.

- This is an expression for acceleration due to gravity at a point P on the surface of the earth having latitude ‘Φ’. At the equator Φ = 0°. Hence ‘g’ is the minimum on the equator. For the poles Φ = 90°. Hence ‘g’ is maximum on the poles.

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