AP Physics 1 Question 314: Answer and Explanation

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Question: 314

2. If a hole were dug through the center of a planet and a ball dropped into the hole, which of the following best describes the motion that the ball would undergo? Assume the ball is indestructible and the planet is a perfect sphere.

  • A. It would continuously gain speed and eventually escape the gravitational pull of the planet.
  • B. It would fall to the center of the planet and get stuck there because gravity is always pulling things toward the center of the planet.
  • C. It would fall to the other end of the hole, come to a momentary stop, fall back to the starting location, and then repeat this back-and-forth motion indefinitely.
  • D. None of the above is correct.

Correct Answer: C

Explanation:

C

Consider the situation from the perspective of conservation of energy. When it is initially dropped on one end of the planet, the ball has some amount of potential energy and no kinetic energy. When it reaches the center of the Earth, it will have no more potential energy, so all of that energy is now kinetic. Due to inertia, the ball will continue in that direction until the energy has again been converted entirely to potential energy. This would happen just as it reaches the other end of the hole. At that point, it would fall again and the process would repeat infinitely. This is exactly the same motion as an ideal spring system.