In this case if the velocity is too low, it might not feel a normal force at all, which means losing contact with the track.
How do we find the minimum height in terms of r.
Initial height can be defined as the minimum height attained by any object during its motion.
Using the energy conservation found in the first part, we can calculate the minimum height.
mgh = mg2R+ ½ mv2
mgh = mg2R + ½ m(gR)
gh = g2R + ½ (gR)
h = 2R + ½ R
h = 5 R/ 2
Hence, the given height will be h = 5 R/2.
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