A roller coaster car (mass = M) is on a track that forms a circular loop (radius = r) in the vertical plane.?

Question

If the car is to just maintain contact with the track at the top of the loop, what is the minimum value for its speed at the point?

Answer 1

at the top force acting downward is mg and force acting upwards is mv^2/r
mg=mv^2/r
g=v^2/r
v=(gr)^1/2
note it does't depend upon mass M