Final answer:
Acceleration due to gravity is the same for a lead and a wooden ball of the same size when dropped (option c), regardless of the difference in their mass, as gravitational acceleration is constant for any object in free fall near the surface of Earth if air resistance is negligible.
Step-by-step explanation:
When two objects, a lead ball and a wooden ball of the same size, are dropped, the acceleration due to gravity is the same for both balls. This is because acceleration due to gravity is independent of the mass of the objects. According to Newton's second law, the net force on an object is responsible for its acceleration. In the case of free fall, if air resistance is negligible, the only force acting on the objects is the gravitational force, which causes them to accelerate at the same rate towards Earth's center.
The gravitational force acting on the lead ball will indeed be larger than that on the wooden ball because the former has a greater mass. However, Newton's second law also tells us that the force is equal to mass times acceleration (F = ma), so a larger force is needed to accelerate the more massive lead ball. This increased force exactly compensates for the larger mass, resulting in the same acceleration for both balls. The correct answer is therefore c. The acceleration due to gravity is the same for both balls.