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

Step 1: Understanding the Concept:
The translational motion of the center of mass of a mechanical system depends entirely and only on the net external force applied to it.
Internal forces between particles inside the body cannot alter the velocity or the state of motion of the center of mass.
Step 2: Key Formula or Approach:
According to Newton's Second Law applied to a system of particles, the net external force governs the acceleration of the center of mass: $F_{\text{ext}} = M a_{\text{cm}}$.
If $F_{\text{ext}} = 0$, it directly implies that $a_{\text{cm}} = 0$.
Step 3: Detailed Explanation:
The problem explicitly states that the external force acting on the body is zero ($F_{\text{ext}} = 0$).
Substituting this into the dynamic equation yields an acceleration of zero for the center of mass ($a_{\text{cm}} = 0$).
Since acceleration is defined as the rate of change of velocity, a zero acceleration means that the velocity of the center of mass does not change over time.
Therefore, the physical state of motion (velocity) of the center of mass remains perfectly constant.
Step 4: Final Answer:
The correct option is that the state of the center of mass remains constant.