Gravitation - Free Fall and Acceleration due to Gravity

Free Fall: When an object falls towards the Earth solely under the influence of gravitational force, with no other forces (like air resistance) acting on it, it is said to be in a state of free fall.

Acceleration due to Gravity ($g$): During free fall, the object undergoes a uniform acceleration towards the center of the Earth. This acceleration is denoted by $g$ and its value on the surface of the Earth is approximately $9.8 \text{ m/s}^2$.

Calculation of $g$: The value of $g$ is derived from the Universal Law of Gravitation. If $M$ is the mass of the Earth and $R$ is its radius, then $g = \frac{GM}{R^2}$.

Variation of $g$: Earth is not a perfect sphere; it is flattened at the poles and bulges at the equator. Since the radius $R$ is smaller at the poles, the value of $g$ is greater at the poles than at the equator.

Equations of Motion under Gravity: For objects moving under the influence of gravity, the standard equations of motion are used by replacing acceleration $a$ with $g$ and distance $s$ with height $h$.

Sign Convention: When an object is falling downwards, $g$ is taken as positive ($+9.8 \text{ m/s}^2$). When an object is thrown vertically upwards, $g$ is taken as negative ($-9.8 \text{ m/s}^2$) because the motion is against gravity.

Mass vs. Weight: Mass ($m$) is the measure of inertia and remains constant everywhere. Weight ($W$) is the force with which the Earth attracts an object ($W = m \times g$) and varies depending on the value of $g$ at a location.