(a) Prove that bodies starting at the same time `t = 0` from the same point, and following frictionless slopes in different directions in the same vertical plane, all lie in a circle at any subsequent time.
(b) Using the above result do the following problem. A point P lies above an inclined plane of inclination angle `alpha`. P is joined to the plane at number of points by smooth wires, running in all possible directions. Small bodies (in shape of beads) are released from P along all the wires simultaneously. Which body will take least time to reach the plane.

Answer

(b) Body travelling along a line making an angle `(alpha)/(2)` with vertical