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This question belongs to Mechanics thread. It is answered there. However, I have reproduced the same below:
We can use law of conservation of angular momentum and law of conservation of mechanical energy to solve this problem.
Initial angular momentum Li = mvb
Final angular momentum Lf = mVR (assuming that the mass m will just graze the surface of earth, as per requirement of the problem statement).
Initial Potential Energy Ui = 0
Final Potential Energy
Initial Kinetic Energy
Final Kinetic Energy
Substituting the values in and solving for b,
we get
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