Two bodies of masses 1kg and 2kg are lying in xy plane at (-1,2) and (2,4) respectively. What are the coordinates of the center of mass?

Options

A. (1,10/3)
B. (1,0)
C. (0,1)
D. None of these

Explanation

To find the coordinates of the center of mass (CM) of two bodies with given masses and positions, we can follow these steps:

### Step 1: Identify the masses and their positions
- Mass \( m_1 = 1 \, \text{kg} \) is located at point \( A(-1, 2) \).
- Mass \( m_2 = 2 \, \text{kg} \) is located at point \( B(2, 4) \).

### Step 2: Write down the formula for the center of mass
The coordinates of the center of mass \( (x_{cm}, y_{cm}) \) can be calculated using the formula:
\[ x_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \]
\[ y_{cm} = \frac{m_1 y_1 + m_2 y_2}{m_1 + m_2} \]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two masses.

### Step 3: Substitute the values into the formula
- For the x-coordinate:
\[ x_{cm} = \frac{1 \cdot (-1) + 2 \cdot 2}{1 + 2} = \frac{-1 + 4}{3} = \frac{3}{3} = 1 \]

- For the y-coordinate:
\[ y_{cm} = \frac{1 \cdot 2 + 2 \cdot 4}{1 + 2} = \frac{2 + 8}{3} = \frac{10}{3} \]

### Step 4: Combine the results
Thus, the coordinates of the center of mass are:
\[ (x_{cm}, y_{cm}) = \left(1, \frac{10}{3}\right) \]

### Final Answer
The coordinates of the center of mass are \( \left(1, \frac{10}{3}\right) \).

---