This is classical physics. It makes a difference whether the stone is
moving or if the cone is moving. If the cone is moving (and is
frictionless) the stone will accelerate straight down to the cone apex,
there being nothing that can provide a tangential acceleration. If it is
the stone that is moving (and perhaps the problem claims that it is
moving in a circle and not falling down?), then there are two forces:
the weight and the normal force from the surface of the cone. The
vertical component of the normal force balances the weight and the
horizonatal component of the normal provides the centripetal
acceleration.
Jerry Epstein