If the sphere has been raised a height h, its potential energy has increased by mgh. As the pendulum swings, this energy will be transformed into kinetic energy and back again;
150 SOLUTION
and when the sphere rises to its highest point again and comes to rest it will have the same potential energy. Thus the ball must rise to the same height as before, since the fact that the thread meets the bar in no way alters the kinetic energy of the sphere. Therefore, wherever the bar be placed at right angles to the plane of the sketch, provided the distance AB be less than l-h/2, the sphere will rise to the same height h. But if AB be greater than l-h/2, then this will not be possible. But in this case when the sphere reaches its highest point it will have some velocity still (since not all its kinetic energy will have been changed into potential energy). It will continue to move in the same direction and the thread will wind itself round the bar.