Sphere Attached to a String Resting Against a Smooth Wall
When an object is in contact with a wall, it will experience a normal reaction force. If the object is held up by an inelastic string making an anglewith the downwards vertical, the tension in the string will have both vertical and horizontal components. If the system is in equilibrium, the sum of all the components in any direction will be zero, and the moments about any point will balance.
Resolving vertically for the sphere gives (1)
Resolving horizontally for the sphere gives (2)
Taking moments about B gives (3)
Equating (1) and (3) givesso that the line of action ofpasses through the centre of the sphere.