The correct option is (c).
Explanation
The motion of objects under the influence of Earth's gravity is governed by the laws of gravitation and motion. It involves the concepts of free fall, acceleration due to gravity, and the resistance offered by the medium (such as air) through which the object travels.
Statement-wise Analysis:
- Statement 1 is Incorrect.
In a vacuum, there is no air resistance. The acceleration due to gravity ($g$) acts equally on all objects regardless of their mass. According to Galileo's principle of free fall, all objects, whether heavy or light (e.g., a feather and a hammer), fall with the same acceleration and reach the ground simultaneously in a vacuum.
- Statement 2 is Correct.
When objects fall through the atmosphere, air molecules collide with the surface of the object, creating a resistive force known as air resistance or fluid friction. This force opposes the direction of motion and depends on the object's speed, surface area, and shape.
- Statement 3 is Correct.
The gravitational force ($F$) experienced by an object is given by the equation $F = mg$, where $m$ is the mass of the object and $g$ is the acceleration due to gravity. Since $g$ is approximately constant near the Earth's surface, the gravitational force (or weight) is directly proportional to the mass of the object.
Key Takeaway:
While the acceleration due to gravity is independent of an object's mass (causing objects to fall at the same rate in a vacuum), the gravitational force acting on the object is directly proportional to its mass.