The centre of mass of two particles system lies

Options

A. at the midpoint on the line joining the two particles.
B. at one end of line joining the two particles
C. on the line perpendicular to the line joining two particles
D. on the line joining the two particles

Answer

To determine the location of the center of mass of a two-particle system, we can follow these steps:

### Step 1: Understanding the Concept of Center of Mass
The center of mass (COM) of a system of particles is the point where the total mass of the system can be considered to be concentrated. For two particles with masses \( M_1 \) and \( M_2 \), the center of mass can be calculated using the formula:

\[ R_{cm} = \frac{M_1 x_1 + M_2 x_2}{M_1 + M_2} \]

where \( x_1 \) and \( x_2 \) are the positions of the two masses.

### Step 2: Analyzing the Options
We have four options to evaluate:

1. **Midpoint of line joining them**: This is only true if \( M_1 = M_2 \). If the masses are equal, the center of mass will indeed be at the midpoint. However, this is not a general case.

2. **One end of line joining them**: This could be true if one mass is significantly larger than the other. For example, if \( M_1 \) is much greater than \( M_2 \), the center of mass will be closer to \( M_1 \). However, this is also not a general case.

3. **Line perpendicular to line joining them**: This option is incorrect because the center of mass must lie along the line connecting the two masses, not perpendicular to it.

4. **On the line joining two particles**: This is the most general statement. Regardless of the values of \( M_1 \) and \( M_2 \), the center of mass will always lie on the line that connects the two particles.

### Step 3: Conclusion
Based on the analysis, the correct answer is that the center of mass of a two-particle system lies **on the line joining the two particles**.

### Final Answer
The center of mass of a two-particle system lies on the line joining the two particles.

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