The reduce mass of two particles having masses m and 2 m is

Options

A. 2 m
B. 3 m
C. 2 m/3
D. m/2

Explanation

To find the reduced mass of two particles with masses \( m \) and \( 2m \), we can use the formula for reduced mass, which is given by:

\[ \mu = \frac{m_1 m_2}{m_1 + m_2} \]

### Step 1: Identify the masses
Let:
- \( m_1 = m \)
- \( m_2 = 2m \)

### Step 2: Substitute the masses into the formula
Now, substitute \( m_1 \) and \( m_2 \) into the reduced mass formula:

\[ \mu = \frac{m \cdot 2m}{m + 2m} \]

### Step 3: Simplify the numerator and denominator
Calculate the numerator:

\[ m \cdot 2m = 2m^2 \]

Calculate the denominator:

\[ m + 2m = 3m \]

### Step 4: Combine the results
Now, substitute the simplified numerator and denominator back into the formula:

\[ \mu = \frac{2m^2}{3m} \]

### Step 5: Simplify the fraction
Now, simplify the fraction:

\[ \mu = \frac{2m^2}{3m} = \frac{2}{3}m \]

### Final Answer
The reduced mass of the two particles is:

\[ \mu = \frac{2}{3}m \]