Correct Option
The correct option is (a).
Explanation
The force of gravity on Earth is quantified by the acceleration due to gravity ($g$). Its magnitude depends on the mass of the Earth and the distance of the object from the center of the Earth, governed by the universal law of gravitation formula $g = \frac{GM}{R^2}$.
Statement-wise Analysis
- Statement 1 is Correct: The acceleration due to gravity is inversely proportional to the square of the distance from the Earth's center ($R$). As altitude increases, the distance from the center increases. Consequently, the value of $g$ decreases.
- Statement 2 is Incorrect: The Earth is not a perfect sphere; it is an oblate spheroid, meaning it is flattened at the poles and bulges at the equator. The equatorial radius is greater than the polar radius. Since $g$ is inversely proportional to the square of the radius ($g \propto \frac{1}{R^2}$), the value of gravity is minimum at the equator and maximum at the poles. Thus, it is not constant across the surface.
- Statement 3 is Incorrect: Gravity is a central, attractive force directed towards the center of mass. While it provides the centripetal force required for orbital motion (e.g., the Moon orbiting Earth), it is not the cause of the Earth's rotation on its own axis. The Earth's rotation is primarily a result of the conservation of angular momentum retained from the formation of the solar system.
Key Takeaway: The acceleration due to gravity ($g$) is not uniform; it decreases with altitude and depth, and varies across the Earth's surface due to the planet's geoid shape (highest at poles, lowest at equator).