Because the poles are closer to the center of the earth due to the earth's oblateness. that's why the value of g is greater at poles

Introduction:
The gravitational acceleration, denoted as "g," varies depending on the location on Earth's surface. It is greater at the pole compared to the equator. This phenomenon can be explained by several factors.

1. Centrifugal Force:
At the equator, the Earth's rotation causes a centrifugal force that counteracts the force of gravity. Since the equator is farther from the Earth's axis of rotation, this effect is more pronounced. The centrifugal force reduces the net gravitational force experienced by an object, resulting in a smaller value of g at the equator.

2. Oblateness of Earth:
The Earth is not a perfect sphere but is slightly flattened at the poles and bulging at the equator. This shape, known as an oblate spheroid, is caused by the Earth's rotation. The equatorial bulge leads to a larger distance between an object and the center of the Earth, reducing the gravitational force experienced. As a result, g is smaller at the equator compared to the poles.

3. Altitude:
Another factor affecting the value of g is altitude. At higher altitudes, the distance between an object and the center of the Earth increases, resulting in a weaker gravitational force. However, this effect is relatively minor compared to the centrifugal force and oblateness of the Earth.

4. Latitude and Earth's Shape:
The combination of the Earth's oblate shape and the centrifugal force due to rotation creates an asymmetrical distribution of mass. This distribution leads to variations in the gravitational field across the Earth's surface. The force of gravity is stronger at the poles because the distance to the center of the Earth is shorter compared to the equator.

Conclusion:
In summary, the greater value of g at the poles compared to the equator is primarily influenced by the centrifugal force caused by Earth's rotation and the oblateness of its shape. These factors result in variations in the gravitational field and affect the net gravitational force experienced by objects at different locations on Earth's surface.