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