Final answer:
The mass of an object can be canceled out in equations where it appears on both sides, as in the case of gravitational force, leading to a general expression for gravitational acceleration that does not depend on the object's mass.
Step-by-step explanation:
When an equation includes the mass of an object on both sides, it is often possible to cancel the mass, assuming it does not change the nature of the equation or the relationships it represents.
This is commonly seen in physics when deriving formulas for universal concepts that are independent of the mass of the objects involved. For example, in the equation for gravitational force (F = GmM/r^2),
where G is the gravitational constant, M is the mass of a celestial body (like Earth), r is the distance to the center of Earth, and m is the mass of the object experiencing the force, both sides of the equation have m.
Therefore, if we are solving for the acceleration due to gravity (g), we can cancel the mass m from both sides, resulting in g = GM/r^2, which shows that the gravitational acceleration is independent of the mass of the falling object.