Question

If external force acting on a body is zero, centre of mass of body

• A. decreases
• B. remains constant
• C. increases
• D. first increases then decreases

Hint:

Even if a body explodes into multiple fragments due to internal forces, as long as no external force is present, the center of mass of the fragments will continue on its original path undisturbed!

Answer 1

The Correct Option is B

Understanding the Concept:

The question is related to the concept of the motion of the center of mass (COM) in physics. Specifically, it examines the behavior of the center of mass of a body when no external forces are acting on it.

The Center of Mass of a Body:

The center of mass is a point representing the mean position of the matter in a body or system. The motion of the center of mass (COM) of a system of particles is governed by Newton's second law of motion.

Newton's Second Law for the Center of Mass:

According to Newton’s second law, the acceleration of the center of mass is directly proportional to the net external force acting on the system and is given by:

\(F_{\text{ext}} = M \cdot a_{\text{com}}\)

where \(F_{\text{ext}}\) is the external force acting on the system, \(M\) is the total mass of the system, and \(a_{\text{com}}\) is the acceleration of the center of mass.

Analysis of the Given Options:

1. Decreases: If the external force acting on the body is zero, there is no acceleration. Thus, the center of mass does not decrease in velocity on its own.
2. Remains Constant: With zero external force, the acceleration of the center of mass is zero (\(a_{\text{com}} = 0\)). Therefore, the velocity and position of the center of mass remain constant over time. This means the motion of the center of mass does not change if unperturbed by external forces.
3. Increases: Without an external force, there is no increase in acceleration; hence, the velocity or position of the center of mass cannot increase intrinsically.
4. First Increases then Decreases: This option suggests a fluctuation in motion which is not possible without external forces causing acceleration and deceleration.

Conclusion:

The only correct option is "remains constant" because it accurately reflects the state of a system's center of mass when the external forces acting upon it are zero.