Is there a relationship between mass of an object, the distance it falls, and the acceleration of the object?

When you drop an object from a certain height and you have a light object and a heavier object to compare, is there a relationship between the mass of the object, the distance it falls, and the acceleration of the object? What happens if you increase the height of the drop?

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The force of attraction between any object of mass M and the Earth of mass Me is given by F = G*M*Me/r^2 where G is a constant and r is the distance between the object and the center of the Earth. The acceleration of the object of mass M due to this is M*a = G*M*Me/r^2

=> a = G*Me/r^2

This shows that the acceleration due to gravity does not depend on the mass of an object. Any two objects of different mass are accelerated towards the Earth with the same acceleration.

When two objects are dropped from a certain height, if the air resistance is ignored, their acceleration is the same and both fall through the same distance in any given duration of time.

If the height from which the objects are dropped is increased, the acceleration due to gravity remains the same for both of them though it decreases slightly as the radius in the formula provided earlier has increased.

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