Question

which one of the following accurately describes the force of gravity? a) the gravity acceleration has no effect on a body moving in directly the opposite direction of the force of gravity. b) the gravity acceleration is in the same direction as the force of gravity, and thus away from the center of the earth. c) the force of gravity is slightly lower at the bottom of a mountain than it is at the top. d) the gravity acceleration is in the same direction as the force of gravity, and thus toward the center of the earth.

Explanation:

• Option A: Gravity acceleration (due to gravitational force) acts on all bodies near Earth, regardless of their motion direction. A body moving opposite to gravity will still experience gravitational acceleration (e.g., a ball thrown upward still has gravity acting on it, slowing it down), so A is incorrect.
• Option B: The force of gravity (and thus gravitational acceleration) acts toward the center of the Earth (since gravity is the attractive force between the body and the Earth's mass), not away. So B is incorrect.
• Option C: Gravitational force is given by \( F = G\frac{Mm}{r^2} \) (where \( r \) is the distance from the Earth's center). At the bottom of a mountain, \( r \) is smaller (closer to the Earth's center) than at the top. Since gravitational force is inversely proportional to \( r^2 \), a smaller \( r \) means a larger gravitational force (and thus acceleration) at the bottom of the mountain compared to the top. So C is incorrect.
• Option D: By Newton's second law (\( \vec{F} = m\vec{a} \)), the acceleration \( \vec{a} \) due to a force \( \vec{F} \) is in the same direction as the force. The force of gravity on a body near Earth is directed toward the Earth's center, so gravitational acceleration is also toward the Earth's center. Thus, D is correct.

Answer:

D. The gravity acceleration is in the same direction as the force of gravity, and thus toward the center of the earth.