A classical mechanics problem by Miraj Shah
Classical Mechanics
Level
3
Consider a body, attached to a string of length \(r\), to be initially at rest in the vertical plane. It can be proved that if we give the body an initial velocity of \(v>\sqrt{5gr}\), then, the body can make complete revolutions in the vertical plane about the point of suspension.
Let us consider that the body, initially at rest, is given a velocity \(v<\sqrt{5gr}\). If at this value of \(v\) the body eventually hits the point of suspension then we can write:
\[ v^2 = (a+\sqrt{b})gr \; . \]
Find \(a\times b\).
by
Miraj Shah