Question

A motor cyclist drives in a vertical circle inside a 'death well'. What is the necessary condition so that he may not fall down?

Answer 1

For the motorcyclist to not fall down, it is necessary that his velocity at the top most point must be greater than the critical velocity, so that the normal force and the weight acting downwards at the top most point are balanced by the centripetal force.

$Critical$ $velocity$ $at$ $top$ $=\sqrt{gr}$

Where $r$ is radius of vertical circle.