A Tunnel in a Solid Sphere: If a body is released from rest at some distance outside a solid sphere, having a diametrical tunnel along its length, then the body will accelerate due to gravitational force by the sphere. It enters into the tunnel, and inside the sphere the gravity decreases and becomes zero at its centre. To analyse the speed of a body during motion we can use its potential energy and apply work energy theorem to solve the case. See the example video below on same situation for understanding this application –
Motion of a Body along the Axis of a Ring: When a body is released from a point anywhere on the axis of a uniform fixed ring, it starts moving towards the centre of the ring, and due to gravity its speed increases. Similarly if a body is projected from the centre of a ring with some initial speed along the axis, its speed decreases as it moves away from the ring. The analysis of speed of a moving body along the axis of a uniform ring in its gravitational field can be done by using work energy theorem. To see the same analysis in a case, see the example video below –