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?

Question

Aicharya · Accepted Answer

Let velocity at the lowest point is "u" and velocity at the top most point is "v"

At highest point $\frac{m v^{2}}{R} = m g \Rightarrow v = \sqrt{g R}$
now $v^{2} = u^{2} - 2 g (2 R) \Rightarrow u^{2} = 5 g R$
Minimum velocity required is $u = \sqrt{5 g R}$

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it…

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