If the force of gravity acts on all bodies in proportion of their masses, then why does not a heavy body fall faster than a light body?

Question

This is question of gravity

Answer 1

Because a heavier object has a proportionally great inertia.

Answer 2

Mark's explanation is correct, but I thought you might want to see the math behind it.  The weight of an object on the earth is

 

W = mg,

 

where g is the local acceleration of gravity.  Why is g the same for a massive object as for a less massive object?  The universal law of gravitation on the surface of the earth takes the form

 

F = GMm/R²

 

where G is the universal constant of gravitation, M is the mass of the earth, and R is the radius of the earth.  But

 

F = W,

 

so

 

GMm/R² = mg ⇒

 

g = GM/R²

 

Note that g does not depend on the mass of the object sitting on the surface of the earth, although it does depend on the mass of the earth.