The position of centre of mass of a system consisting of two particles of masses `m_(1)` and `m_(2)` seperated by a distance L apart , from `m_(1)` will be :

Options

A. `(m_(1)L)/(m_(1)+m_(2))`
B. `(m_(2)L)/(m_(2)+m_(2))`
C. `(m_(2))/(m_(1))L `
D. `L/2 `

Answer

To find the position of the center of mass of a system consisting of two particles with masses \( m_1 \) and \( m_2 \) separated by a distance \( L \), we can follow these steps:

### Step 1: Define the System
We have two particles:
- Particle 1 with mass \( m_1 \) located at position \( x_1 = 0 \).
- Particle 2 with mass \( m_2 \) located at position \( x_2 = L \).

### Step 2: Write the Formula for Center of Mass
The formula for the center of mass \( R \) of a system of particles is given by:

\[ R = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \]

### Step 3: Substitute the Known Values
Substituting the positions of the particles into the formula:

- For \( x_1 = 0 \) (position of \( m_1 \))
- For \( x_2 = L \) (position of \( m_2 \))

The formula becomes:

\[ R = \frac{m_1 \cdot 0 + m_2 \cdot L}{m_1 + m_2} \]

### Step 4: Simplify the Expression
This simplifies to:

\[ R = \frac{0 + m_2 L}{m_1 + m_2} = \frac{m_2 L}{m_1 + m_2} \]

### Conclusion
Thus, the position of the center of mass from the mass \( m_1 \) is:

\[ R = \frac{m_2 L}{m_1 + m_2} \]