Every Action has an equal and Opposite Reaction,

According to me , This is just an assumption by Newton because he already knowing that Earth has Gravity thought of a thing that is ,

In Space, there is Zero Gravity and if an object is dropped over there without any force , the body remains there at rest stating Newton's first law of Motion that is Inertia and he might have thought that, Since there is no opposing force in Space, so the body remains in rest but the Earth has Gravity so he assumed that there requires one force to control the Gravity , So he assumed the force as Upthrust that is nothing but what he stated as the Reaction Force when the body lies on a table with no force applied on it .

So, there is no proof for this case of Newton's 3rd law example either theorotically or mathematically proof for the Formula he stated that is "R = -mg ".

So, According to me It is just an Assumption without any proof for this case of example of Newton's 3rd law especially .

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