Two points objects of mass 1.5g and 2.5g respectively are a distance of 16cm apart, the center of mass is at distance x from the object of mass 1.5g. Find the value of x

Options

A. `12 cm`
B. `14 cm`
C. `10 cm`
D. `16 cm`

Explanation

To find the center of mass (CM) of two point masses, we can use the formula for the center of mass of a system of particles:

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

Where:
- \( m_1 \) and \( m_2 \) are the masses of the objects,
- \( x_1 \) and \( x_2 \) are their respective positions.

### Step-by-Step Solution:

1. **Identify the masses and their positions**:
- Let \( m_1 = 1.5 \, \text{g} \) (mass of the first object).
- Let \( m_2 = 2.5 \, \text{g} \) (mass of the second object).
- The distance between the two masses is \( 16 \, \text{cm} \).

2. **Assign positions**:
- Assume the position of the first mass \( m_1 \) (1.5 g) is at \( x_1 = 0 \, \text{cm} \).
- Therefore, the position of the second mass \( m_2 \) (2.5 g) will be at \( x_2 = 16 \, \text{cm} \).

3. **Plug values into the center of mass formula**:
\[ x_{cm} = \frac{(1.5 \, \text{g})(0 \, \text{cm}) + (2.5 \, \text{g})(16 \, \text{cm})}{1.5 \, \text{g} + 2.5 \, \text{g}} \]

4. **Calculate the numerator**:
\[ x_{cm} = \frac{0 + 40 \, \text{g cm}}{4 \, \text{g}} = \frac{40 \, \text{g cm}}{4 \, \text{g}} = 10 \, \text{cm} \]

5. **Determine the distance \( x \)**:
- The center of mass is at a distance \( x = 10 \, \text{cm} \) from the object of mass \( 1.5 \, \text{g} \).

### Final Answer:
The value of \( x \) is \( 10 \, \text{cm} \).

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