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Question

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?
  1. gR
  2. 2gR
  3. 5gR
  4. 3gR

A
gR
B
3gR
C
5gR
D
2gR
Solution
Verified by Toppr

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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