Two particles of masses 1kg and 2kg are located at `x=0` and `x=3m`. Find the position of their centre of mass.

Options

A. 2m from 1 kg
B. 2m from 2 kg
C. 1m from 1 kg
D. none of these

Explanation

To find the position of the center of mass of two particles with given masses and positions, we can follow these steps:

### Step 1: Identify the masses and their positions
- Let \( m_1 = 1 \, \text{kg} \) (mass of the first particle)
- Let \( x_1 = 0 \, \text{m} \) (position of the first particle)
- Let \( m_2 = 2 \, \text{kg} \) (mass of the second particle)
- Let \( x_2 = 3 \, \text{m} \) (position of the second particle)

### Step 2: Use the formula for the center of mass
The formula for the center of mass \( x_{cm} \) of two particles is given by:

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

### Step 3: Substitute the values into the formula
Substituting the values we have:

\[ x_{cm} = \frac{(1 \, \text{kg} \cdot 0 \, \text{m}) + (2 \, \text{kg} \cdot 3 \, \text{m})}{1 \, \text{kg} + 2 \, \text{kg}} \]

### Step 4: Calculate the numerator and denominator
Calculating the numerator:

\[ 1 \cdot 0 + 2 \cdot 3 = 0 + 6 = 6 \]

Calculating the denominator:

\[ 1 + 2 = 3 \]

### Step 5: Final calculation of \( x_{cm} \)
Now, substituting back into the equation:

\[ x_{cm} = \frac{6}{3} = 2 \, \text{m} \]

### Conclusion
The position of the center of mass is \( 2 \, \text{m} \) from the origin (where the 1 kg mass is located).