If you drop two balls of the same radius, they will accelerate toward the ground. If one ball is more massive than another, its acceleration a. will be larger than that of the less massive ball. b. will be smaller than that of the less massive ball. c. will be the same as that of the less massive ball. d. will depend on other factors.

When an object is in free fall, it experiences a force due to gravity. This force is responsible for the object's acceleration towards the Earth. This particular acceleration is called the 'acceleration due to gravity' and is denoted by the symbol 'g'.
Most importantly, the value of 'g' near the surface of the Earth is approximately 9.8 m/s². This value is crucial because it tells us how quickly an object speeds up as it falls.
Expressing this in formula form, for any object falling solely under the influence of gravity, the force acting on it is:

• Force (F) = Mass (m) x Acceleration due to gravity (g)

This relationship illustrates that the force acting on an object is directly proportional to its mass and the acceleration due to gravity.

Free fall describes the motion of objects falling solely under the influence of gravity. During free fall, no other forces are acting on the object (like air resistance).

Some key characteristics of free fall include:

• All objects, regardless of their mass, will experience the same acceleration, 'g'. This means they fall at the same rate in the absence of air resistance.
• The velocity of the object increases as it continues to fall due to the constant acceleration.
• The time it takes to fall is determined by the height and initial velocity if any.

Consider this: if you drop a feather and a hammer on the Moon (where there is no air), they will both hit the ground simultaneously. This dramatic demonstration was shown by an astronaut during the Apollo missions.
One can use the equations of motion to predict how long it will take for an object to reach the ground in free fall.

One critical and fascinating idea in physics is that the acceleration due to gravity is independent of mass. This means that whether an object is heavy or light, if it is in free fall, it will accelerate towards the ground at the same rate.

This concept was first famously tested by Galileo, who is said to have dropped two spheres of different masses from the Leaning Tower of Pisa. The spheres hit the ground simultaneously, showing that their accelerations due to gravity were identical.
Mathematically, this can be seen through Newton’s Second Law:

Newton's Second Law:

• Acceleration (a) = Force (F) / Mass (m)

Since the force of gravity is proportional to mass (F = mg), when divided by the object's mass, the mass cancels out:

• a = (mg) / m = g

This cancellation shows that the acceleration (a) is equal to 'g', irrespective of mass. This mass independence is a cornerstone of classical mechanics and helps simplify the understanding of how objects move under gravity.