Question

Proof that the value of g is independent of the mass of the object in Earth's gravitational field (Proving that g depends only on the mass of the Earth (M) and the distance of the object from the center of the Earth, r).

A) Gravitational force depends on the density of the object.
B) Gravitational force depends on the object's volume.
C) Gravitational force depends on the object's color.
D) Gravitational force depends only on the mass of the Earth (M) and the distance from the center of the Earth (r).

Answer 1

The value of gravitational acceleration (g) is independent of the mass of the object because when we apply Newton's law of gravitation and his second law of motion, the mass of the object cancels out, resulting in g = GM/r^2.

Step-by-step explanation:

The proof that the acceleration due to gravity (g) is independent of the mass of the object involves using Newton's law of gravitation and his second law of motion. The gravitational force is given by F = G(Mm/r2), where M is the mass of the Earth, m is the mass of the object, r is the distance to the center of the Earth, and G is the gravitational constant. According to Newton's second law, F = ma, where a is the acceleration. Combining these equations gives us ma = G(Mm/r2). The mass m of the object cancels out, leaving us with the equation for g: g = GM/r2, which depends only on the mass of the Earth (M) and the distance from the center of the Earth (r).