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?

Step-by-step solution

Let velocity at the lowest point is "u" and velocity at the top most point is "v" At highest point m v 2 R = m g ⇒ v = g R now v 2 = u 2 − 2 g ( 2 R ) ⇒ u 2 = 5 g R Minimum velocity required is u = 5 g R