Just wondering if this statement is true, GMm/R^2=v^2/R
It can be. Like most equations, it applies to some things and not others.
Yes it applies when circular motion is caused by Gravitation as in satellite or planetary motion. The right side is the Centripetal Force representing the reason the object is not moving linearly due to inertia.
You did forget the m for mass on the right side needed to make the acceleration a Force.
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