Final answer:
The false statement about this system is that it becomes more stable after the boulder falls.
Step-by-step explanation:
In this system, the potential energy of the boulder is higher when it is on top of the mountain compared to when it is on the ground, so option A is true, not false.
As the boulder falls down the mountain, potential energy is converted to kinetic energy, so potential energy decreases and kinetic energy increases, which means that option E is true, not false.
Therefore, the false statement about this system is option B. The system does not become more stable after the boulder falls. In fact, the system reaches its most stable state when the boulder is at the bottom of the mountain where potential energy is at its minimum and kinetic energy is at its maximum.