The correct statement regarding the acceleration of each object due to gravity, according to Newton's second law (F = ma), is:
a. The object with a larger mass (Earth) will have LESS acceleration than the object with the smaller mass (the rock).
Here's the reasoning:
Newton’s law of universal gravitation states that the force between two masses is equal (action-reaction pairs), but according to F = ma, the acceleration produced by a force is inversely proportional to mass. Since the Earth has a much larger mass than the rock, it experiences much less acceleration in response to the gravitational force acting on it compared to the rock, which has a smaller mass and thus experiences a higher acceleration.
To elaborate:
- If the gravitational force acting between the two is the same, we can set this up as: \[ F = m_\text{Earth} \cdot a_\text{Earth} = m_\text{rock} \cdot a_\text{rock} \]
Since \(m_\text{Earth} \) is much larger than \(m_\text{rock}\), the acceleration \(a_\text{Earth}\) will be very small compared to the acceleration \(a_\text{rock}\). Hence, the rock will fall toward the Earth with greater acceleration than the Earth will move toward the rock.
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