physics, rotational motion, gravitation, question is in description

Question

Gravitational force acts on all bodies in proportion to their masses. Why, then, doesn’t a heavy body fall faster than a light body?

Answer 1

The gravitational force between two masses (say the Earth M_E, and a ball M_B) is given by Newton's Law of Universal Gravitation, F = GM_EM_B/r², where G is the Universal Gravitational Constant, and r is the distance between the center-of-mass of the two objects. So, if ball 2 has twice the mass of ball 1, then the gravitational force on ball 2 is twice that on ball 1.

The acceleration depends upon both the force and the mass, F = ma. Since F₂ is twice F₁, and M₂ is twice M₁, the acceleration on the two different masses is the same.