According to Newton second law of motion, if the mass of an object is kept constant, its acceleration is ______.

Introduction / Context:

Newton second law of motion is one of the most fundamental relations in mechanics, connecting force, mass and acceleration. Understanding how acceleration depends on force and mass helps in predicting the motion of objects under different loads. This question focuses on how acceleration changes when only the applied force is varied and the mass of the object is kept constant.

Given Data / Assumptions:

• Newton second law is expressed as F = m * a.
• The mass m of the object is constant in the situation described.
• We consider net force acting along the line of motion.
• We want the proportionality relationship between acceleration a and applied force F under these conditions.

Concept / Approach:

From F = m * a, we can express acceleration as a = F / m. If the mass m is fixed, then a is directly proportional to F. That means if you double the force, the acceleration doubles; if you halve the force, the acceleration halves. Inverse proportionality to mass appears when you keep force constant, not when you keep mass constant. Therefore, among the options, only direct proportionality to applied force correctly describes the dependence of acceleration under the given condition.

Step-by-Step Solution:

Verification / Alternative check:

Suppose an object of mass 2 kg is pushed by a force of 4 N; then its acceleration is a = 4 / 2 = 2 m s^-2. If the force is increased to 8 N while mass remains 2 kg, the new acceleration is a = 8 / 2 = 4 m s^-2, which is double the previous value. This simple numerical example confirms that acceleration doubles when force doubles, consistent with direct proportionality between acceleration and force when mass is unchanged.

Why Other Options Are Wrong:

Option A (inversely proportional to the applied force): This would mean that increasing force reduces acceleration, which contradicts both the formula and physical experience.

Option B (inversely proportional to the mass of the object): While acceleration is indeed inversely proportional to mass, this statement is irrelevant when mass is fixed; the question specifically asks about dependence on force for a given mass.

Option C (directly proportional to the mass): This is the opposite of the correct relationship; for a given force, larger mass produces smaller acceleration.

Option E (independent of the applied force): This would imply that changing the force has no effect on acceleration, which clearly contradicts Newton second law and everyday observations.

Common Pitfalls:

Many students memorise that acceleration is directly proportional to force and inversely proportional to mass but sometimes forget which variable is being held constant in a particular question. Always start from the equation F = m * a and solve for the quantity of interest. If mass is constant, focus on how changing F changes a. If force is constant, focus on how changing m changes a. This systematic approach prevents confusion about proportionality statements.

Final Answer:

For a given mass, acceleration is directly proportional to the applied force.