What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?
√gR
√2gR
√5gR
√3gR
A
√gR
B
√3gR
C
√5gR
D
√2gR
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Solution
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To just complete the circle, at the highest point, tension is zero and the gravitational force provides the necessary centripetal force.
Hence, mv2topR=mg.............(i)
Applying conservation of energy at the top and bottom points,
12mv2bottom=mg×2R+12mv2top.........(ii)
Substituting mv2top from (i) in (ii) and solving,
vbottom=√5gR
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