If I allow two bodies of different masses to fall freely from same height towards the earth, how can I prove that the acceleration produced in both was constant and equal to gravity.
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I'm not exactly sure what you are asking. If you're wondering about how we know that bodies of different masses fall at the same rate if we ignore other factors like air resistance, then you might want to take a look at experiments like these.
If you are interested in how we arrive at the conclusion that the acceleration is equal to gravity, we can calculate the gravitational acceleration we would expect based on the masses of the earth and the falling bodies and compare that with the experimental result. More explicitly, ignoring the relative differences in size between the objects, we start by calculating the force $F$ between the earth with mass $m_{\mathrm{earth}}$ and an object with mass $m_{\mathrm{object}}$ as $$F=G\frac{m_{\mathrm{earth}}\,m_{\mathrm{object}}}{r^2}$$, where $G$ is the gravitational constant and $r$ is the distance between the objects. Since $F=m_{\mathrm{object}}\,a$, we can rearrange to $$a=g=G\frac{m_{\mathrm{earth}}}{r^2}$$, where $g$ is now the acceleration the object feels due to earth's gravity.
If you are interested in how we arrive at the conclusion that the acceleration is constant, well, we measure the time it takes the objects to fall certain distances and calculate the acceleration from there (it would only be approximately constant for small distances, but certainly as measured by experiments like the one posted above).
Graumagier
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