The correct option is (a).
Explanation
The acceleration due to gravity ($g$) is derived from Newton's Law of Universal Gravitation. It represents the acceleration experienced by an object solely due to the gravitational pull of a massive body, such as the Earth.
- Statement 1 is correct: The mathematical expression for acceleration due to gravity on the surface of the Earth is given by the formula:
$g = \frac{GM}{R^2}$
where $G$ is the universal gravitational constant, $M$ is the mass of the Earth, and $R$ is the radius of the Earth. Consequently, the value of $g$ is directly proportional to the mass of the Earth. - Statement 2 is incorrect: Atmospheric pressure is the force exerted per unit area by the weight of the air above a surface. It is a thermodynamic variable and does not influence the gravitational field strength ($g$). While atmospheric conditions may cause air resistance (drag) that opposes motion, the intrinsic value of acceleration due to gravity remains unaffected by pressure.
- Statement 3 is incorrect: As indicated by the formula $g = \frac{GM}{R^2}$, the variable for the mass of the falling object ($m$) is absent. This signifies that acceleration due to gravity is independent of the mass of the body being attracted. In the absence of air resistance, all objects fall with the same acceleration regardless of their mass.
Key Takeaway: Acceleration due to gravity ($g$) depends exclusively on the mass and radius of the source body (Earth) and is independent of the properties (mass, shape, or density) of the falling object.