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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.

Sofia
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    possible duplicate of Why do two bodies of different masses fall at the same rate (in the absence of air resistance)? – Javier Feb 22 '15 at 20:15
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    Philosopher: "If I allow two bodies [...] of different masses [...] to fall freely from same height towards earth then how can I prove that the acceleration produced in both was constant and equal to gravity." -- This follows immediately from the very definition of "equal gravimetric height with respect to the Earth's surface". So, in case that's what you meant be "same height towards earth", then there is the requested proof. (I may still expand this comment into an answer ...) – user12262 Feb 22 '15 at 20:21
  • OK go on with that –  Feb 22 '15 at 20:25
  • I think you may need to explain this question. If two things follow the same trajectory then their accelerations are equal by definition. Where's the mystery? – DanielSank Feb 22 '15 at 20:59
  • @Philosopher to what else can be equal the acceleration than to the gravitational acceleration? Are there other fields action on the objects? – Sofia Feb 23 '15 at 01:03
  • I'm voting to close this question as off-topic because the question is of a too low level in physics. – Sofia Feb 23 '15 at 01:03

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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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  • Graumagier: "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" -- Namely: How, explicitly? No mentioning of "height(s)" ?? "and compare that with the experimental result." -- Accordingly, we'd arrive case by case at conclusions whether (or not); but not necessarily "at the conclusion that [...]". – user12262 Feb 22 '15 at 21:47
  • Of course the distance plays a role in determining gravitational attraction, I've added some additional info. And sure, we would do the experiment to check whether (or not) we'd arrive at that conclusion ;) – Graumagier Feb 22 '15 at 22:21
  • Graumagier: Thanks. With this topic I just can't help caring especially about the "philosophical" rigor ... – user12262 Feb 22 '15 at 22:47
  • If that topic happens to be science I'm inclined to agree ;) – Graumagier Feb 22 '15 at 22:50