Question

If heavier bodies are attracted more strongly by the earth, why don't they fall faster than the lighter bodies?

Answer 1

We know that acceleration due to a force on a body of mass in given by $a=\frac{F}{m}$.
If F is the gravitational force acting on a body of mass m, then a is the acceleration of a free falling body.

This force is given as $F=G\frac{Mm}{R^2}$.
Here, M is the mass of the Earth; G is the universal gravitational constant and R is the radius of the Earth.
∴ Acceleration due to gravity, $a=\frac{F}{m}=\frac{GM}{R^2}$
From the above relation, we can see that acceleration produced in a body does not depend on the mass of the body. So, acceleration due to gravity is the same for all bodies.