The correct option is (b).
Explanation
The acceleration due to gravity ($g$) is the acceleration gained by an object due to the gravitational force. Its value on the surface of the Earth depends on the Earth's mass and radius.
- Statement 1 is Incorrect: The Earth is not a perfect sphere; it is an oblate spheroid. It is flattened at the poles and bulges at the equator due to its rotation. Consequently, the distance from the center of the Earth to the surface varies, meaning $g$ is not constant everywhere on the surface.
- Statement 2 is Correct: The value of acceleration due to gravity is given by the formula $g = \frac{GM}{R^2}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, and $R$ is the radius. Since the equatorial radius ($R_e$) is larger than the polar radius ($R_p$), and $g$ is inversely proportional to the square of the radius ($g \propto \frac{1}{R^2}$), the value of $g$ is greater at the poles (where $R$ is minimum) than at the equator (where $R$ is maximum).
- Statement 3 is Incorrect: Based on the inverse square law ($g \propto \frac{1}{R^2}$), as the radius ($R$) increases, the value of $g$ decreases. Therefore, $g$ is lowest at the equator where the radius is largest.
Key Takeaway: The value of $g$ is not uniform across the Earth; it is maximum at the poles and minimum at the equator due to the Earth's geoid shape (oblate spheroid).