I am unable to derive the equation for the minimum velocity required to make a round in a loop. Can you help me ?

At first, I have to derive the expression for minimum velocity in a circular loop like this

Will the expression be same in this case as well?

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TopNewestUse conservation of energy to determine the kinetic energy (and speed) at any point on the circle, assuming the object starts on the bottom. The kinetic energy gives the centripetal force, which is a combination of the gravity component in the radial direction, plus a reaction force from the surface. This reaction force can't be negative (the surface can push but can't pull). Therefore, that is the requirement. Determine the minimum initial speed such that the reaction force is never negative, when going from the bottom to the top.

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