According to Newton second law of motion, for a given applied force, the acceleration of an object is inversely proportional to its ______.

Introduction / Context:

Newton second law of motion is a fundamental principle in mechanics, relating force, mass and acceleration. Many exam questions check whether you understand how acceleration depends on these variables. This particular question focuses on the relationship between acceleration and mass when the applied force is fixed, which gives insight into why heavier objects are harder to accelerate than lighter ones.

Given Data / Assumptions:

• The law is expressed as F = m * a, where F is net force, m is mass and a is acceleration.
• The applied force is kept constant in this question.
• We must identify the quantity to which acceleration is inversely proportional under this condition.
• Other quantities like density, volume and surface area are not directly part of the basic equation.

Concept / Approach:

From Newton second law, F = m * a. Rearranging this equation for acceleration gives a = F / m. If the force F is constant, acceleration a varies inversely with mass m. That means that as mass increases, acceleration decreases, and as mass decreases, acceleration increases, for the same applied force. This is the mathematical meaning of inverse proportionality. Density, volume and surface area may influence motion through other effects like air drag or buoyancy, but the direct inverse relationship comes from mass in the F = m * a equation.

Step-by-Step Solution:

Verification / Alternative check:

You can verify this by considering two objects, one with mass 1 kg and another with mass 2 kg, both subjected to the same force, for example F = 10 N. For the 1 kg object, a = 10 / 1 = 10 m s^-2. For the 2 kg object, a = 10 / 2 = 5 m s^-2. The heavier object accelerates less, exactly half as much, confirming that acceleration decreases as mass increases. This simple numerical example matches the inverse proportionality found from the formula.

Why Other Options Are Wrong:

Option A (density): Density is mass per unit volume and does not appear directly in the basic law F = m * a. It can influence motion in other contexts but is not the quantity with which acceleration has the stated inverse relationship in this simple situation.

Option B (volume): Volume alone does not determine acceleration; two objects with the same volume can have very different masses and therefore different accelerations under the same force.

Option C (applied force): Acceleration is directly proportional to force, not inversely proportional, when mass is kept constant.

Option E (surface area): Surface area can affect forces like air resistance, but it is not part of the base equation relating net force, mass and acceleration.

Common Pitfalls:

A common confusion is mixing up direct and inverse proportionality. It helps to remember that a quantity in the numerator of a fraction (like F in F / m) is directly proportional, while a quantity in the denominator (like m) is inversely proportional. Writing out the rearranged equation a = F / m and identifying which variable is changing makes it easy to see that acceleration varies inversely with mass when force is fixed.

Final Answer:

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