Mass of the object
Explanation
The acceleration due to gravity ($g$) is derived from Newton's Law of Universal Gravitation. The force of gravity ($F$) acting on an object of mass $m$ situated on the surface of the Earth (mass $M$ and radius $R$) is given by:
$F = \frac{GMm}{R^2}$
According to Newton's Second Law of Motion, force is also defined as the product of mass and acceleration ($F = mg$). Equating the two expressions:
$mg = \frac{GMm}{R^2} \implies g = \frac{GM}{R^2}$
Where $G$ is the universal gravitational constant.
Analysis of Options:
- Radius of the earth Radius of the earth: The formula shows that $g$ is inversely proportional to the square of the radius ($R^2$). Variations in the Earth's radius (due to its oblate spheroid shape) cause $g$ to vary from the poles to the equator.
- Mass of the earth Mass of the earth: The formula indicates that $g$ is directly proportional to the mass of the Earth ($M$).
- Mass of the object Mass of the object: The mass of the object ($m$) cancels out during the derivation. Therefore, $g$ is independent of the mass, shape, or size of the object falling (ignoring air resistance).
- Altitude: As altitude increases, the distance from the center of the Earth increases ($R + h$). Since $g$ is inversely proportional to the square of the distance, the value of $g$ decreases with an increase in altitude.
Key Takeaway:
Acceleration due to gravity depends solely on the mass and radius of the celestial body exerting the force, not on the mass of the object experiencing the force.