Is It Uniform Acceleration?

Assume that Earth is a perfect sphere with radius \(R.\) The time \(T\) an object takes to fall to the ground from rest from a height of \(R\) above the ground is given by \[T=\sqrt{\frac Rg}\left(A+\frac {\pi^B}C\right),\] where \(A,B,C\) are positive integers.

Find \(A+B+C.\)

Note: Consider only gravity, and forget about atmospheric effects, air resistance, etc.

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