Centre Of Mass

To determine the center of mass of the system, we use the formula for the center of mass ( ) of a two-particle system:

X_cm =

Where:

• m₁ and m₂ are the masses of the particles.
• x₁ and x₂ are their respective distances from the origin.

Let's evaluate the given answer choices:

The formula for the center of mass is correctly represented by option (C), .

The centre of mass (CM) of a system is the weighted average position of all the masses in the system. It depends on the mass distribution, shape, and size of the system. However, it is independent of the coordinate system.
That is, the position of the centre of mass will remain the same regardless of which coordinate system you use. The centre of mass is not influenced by the choice of origin, and it does not necessarily lie within the body; it can lie outside the body in certain cases (e.g., a ring).
Thus, option (C) is the correct answer.