Question

A small ball is rolled with speed `u` from piont A along a smooth circular track as shown in figure. If `x=3R`, then

Determine the required speed u so that the ball returns to A, the point of projection after passing through C, the highest point.

Answer 1

We determine the velocity at `C` so that it reaches `A` along a parbolic trajectory, then applying the law of conservation of energy to the motion `ABC` (as non-conservative force are absent)
`v=` velocity at point `C=(3)/(2)sqrt(gR)`
applying conservation of energy from `A` to `C`
`(1)/(2)mu^(2)=2mgR+(1)/(2)mv^(2)`
`rArr u=(5)/(2)sqrt(gR)`