The acceleration of a free fall due to gravity is not a constant everywhere on the Earth's surface because

Analysis

The question asks why the acceleration due to gravity ($g$) varies across different points on the Earth's surface. We know that $g$ is defined by the formula:

Where:

• $G$ is the universal gravitational constant.
• $M$ is the mass of the Earth.
• $R$ is the distance from the center of the Earth to the point on the surface.

Concept Explanation

The value of $g$ depends primarily on the distance ($R$) from the Earth's center. If the Earth were a perfect sphere, $R$ would be constant everywhere, and $g$ would be the same. However, the Earth is not a perfect sphere; it is an oblate spheroid. It bulges at the equator and is flattened at the poles.

Because of this shape:

1. At the poles: The surface is closer to the center of the Earth (smaller $R$). Since $g$ is inversely proportional to $R^2$, a smaller $R$ results in a higher value of $g$.
2. At the equator: The surface is further from the center of the Earth (larger $R$). A larger $R$ results in a lower value of $g$.

Step-by-Step Solution

1. Identify the variables: In the formula $g = \frac{GM}{R^2}$, $G$ and $M$ are constant for the Earth.
2. Analyze the geometry: The Earth's radius is not uniform. The equatorial radius is larger than the polar radius due to the Earth's rotation during its formation.
3. Apply the relationship: Since $g \propto \frac{1}{R^2}$, the variation in the radius ($R$) directly causes the variation in the acceleration due to gravity ($g$).
4. Evaluate the options: While the rotation of the Earth (Option D) does contribute to the apparent gravity, the primary physical reason for the variation in the gravitational field itself across the surface is the Earth's non-spherical (elliptical) shape.

Conclusion

The elliptical shape (oblate spheroid) means the distance from the Earth's center varies with latitude, leading to the observed differences in $g$.

Exam Tip

Remember the "Pole-Equator" rule: Gravity is strongest at the poles (where you are closer to the center) and weakest at the equator (where you are further away). If you ever forget this, just remember that the Earth is "squashed" at the poles, making you closer to the core!