Centre Of Mass

The center of mass (COM) of three particles of equal mass can be calculated using the formula: Since all particles have equal mass, the formula simplifies to: Where: - - - Substituting the values: Thus, the correct answer is (A) 2 cm.

Concept:

Step 1: Take direction carefully.
Let acceleration of 2 kg mass be positive. Direction → towards 2 kg mass.

Concept: Motion of centre of mass depends only on external forces.

Step 1: During explosion.
Explosion is internal force.

Step 2: External force.
Only gravity acts externally.

Step 3: Conclusion.
Centre of mass continues original parabolic path.

Step 1: Formula for Centre of Mass Velocity


Step 2: Assume Directions
Since only speed is given, assume opposite directions:


Step 3: Substitute Values


Step 4: Simplify


Step 5: Interpret Result
Negative sign indicates motion towards heavier mass (120 g).

Step 6: Final Answer

Step 1: Understanding the Concept:
The dynamics of a system of particles are governed by Newton's Second Law applied to the center of mass. The acceleration of the center of mass ( ) depends \textit{only} on the net external force acting on the entire system.
Step 2: Key Formula or Approach:

If the net external force is zero, then , regardless of internal interactions.
Step 3: Detailed Explanation:
Consider the two masses and as forming a single closed system.
The only force mentioned is the mutual gravitational attraction between them.
Mass exerts a gravitational pull on mass . By Newton's Third Law, mass exerts an equal and opposite gravitational pull on mass .
These gravitational forces are purely internal to the two-mass system. They are an action-reaction pair that sum to zero when considering the system as a whole.
Assuming there are no other outside forces acting on the masses (like gravity from a planet, friction, etc., as none are stated), the net external force on the system is exactly zero.

According to the equation of motion for the center of mass:



Even though the individual masses accelerate towards each other, their center of mass remains perfectly stationary (or continues in uniform motion if it was already moving).
Step 4: Final Answer:
The acceleration of their centre of mass is zero.

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: .
If , it directly implies that .
Step 3: Detailed Explanation:
The problem explicitly states that the external force acting on the body is zero ( ).
Substituting this into the dynamic equation yields an acceleration of zero for the center of mass ( ).
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.