When a ball at rest is dropped, can it rebound to a greater height than its original height?
When the ball falls, some of its gravitational potential energy is converted to other forms of energy, such as kinetic energy and rotational energy.
When it rebounds, these other forms of energy is converted back to gravitational potential energy.
During this process, some of its energy is lost from friction, heat, sound, etc. This means that it cannot be rebound back to its original height.
However, this only means that its final gravitational potential energy
But, usually, the ball will not be rebound to a height greater than its original height.