According to Newton's Second Law of Motion, for a given constant force, the acceleration of an object is inversely proportional to which property of the object?

Introduction / Context:
Newton second law of motion provides a quantitative link between force, mass and acceleration. It tells us not only that force causes acceleration but also how the magnitude of acceleration depends on the applied force and the mass of the object. This question focuses on the relationship between acceleration and an object properties when the applied force is kept constant.

Given Data / Assumptions:

• We consider a constant net force acting on an object.
• Newton second law is written in the form F = m * a.
• We investigate how acceleration a changes when mass m changes, while F remains fixed.
• Other properties like density and volume may vary but are not included explicitly in the law.

Concept / Approach:
From F = m * a, we can write acceleration as a = F / m. This expression directly shows that for a fixed F, acceleration is inversely proportional to mass. That is, if the mass doubles, acceleration halves; if the mass is reduced, acceleration increases. Density and volume may influence mass, but the fundamental inverse proportionality is between acceleration and mass, not between acceleration and density or volume directly.

Step-by-Step Solution:
Step 1: Start with Newton second law: F = m * a. Step 2: Rearrange to express acceleration: a = F / m. Step 3: For a given constant force F, this becomes a ∝ 1 / m. Step 4: This means that as mass increases, acceleration decreases proportionally, and vice versa. Step 5: Note that density is mass per unit volume and does not appear directly in this formula. Step 6: Therefore, the quantity with which acceleration is inversely proportional, for given force, is the mass of the object.

Verification / Alternative check:
Everyday experience supports this idea. It is harder to accelerate a heavy object than a light one with the same push. For example, pushing an empty trolley is easier than pushing a loaded trolley, because the loaded trolley has more mass and thus smaller acceleration for the same applied force. In physics labs, experiments with carts and known masses confirm that acceleration varies inversely with the total mass.

Why Other Options Are Wrong:
Density: While density relates mass and volume, acceleration depends directly on total mass, not on density alone. Two objects with different densities but the same mass will have the same acceleration for a given force.

Volume: An object volume does not directly appear in F = m * a. Large but light objects and small but heavy objects can have very different accelerations depending on their mass.

Magnitude of the applied force: For a given force, acceleration is directly proportional to F, not inversely. The question explicitly states that force is fixed, so we focus on mass.

Common Pitfalls:
Students sometimes think that heavier objects fall faster or accelerate less only because of gravity, mixing everyday impressions with the precise law. To avoid confusion, always go back to the formula a = F / m. When F is fixed, any change in m must be reflected inversely in a. This logic works for all types of net forces, not just gravity.

Final Answer:
For a given force, acceleration is inversely proportional to the mass of the object.