Two bodies of different masses `2kg` and `4kg` are moving with velocities `2m//s` and `10m//s` towards each other due to mutual gravitational attraction. Then the velocity of the centre of mass is

Options

A. `5 ms^(-1)`
B. `6 ms^(-1)`
C. `8 ms^(-1)`
D. zero

Explanation

To solve the problem of finding the velocity of the center of mass for two bodies of different masses moving towards each other, we can follow these steps:

### Step 1: Identify the masses and velocities
We have two bodies:
- Mass of the first body, \( m_1 = 2 \, \text{kg} \) with velocity \( v_1 = 2 \, \text{m/s} \) (towards the right)
- Mass of the second body, \( m_2 = 4 \, \text{kg} \) with velocity \( v_2 = -10 \, \text{m/s} \) (towards the left, hence negative)

### Step 2: Use the formula for the velocity of the center of mass
The formula for the velocity of the center of mass \( V_{cm} \) is given by:
\[ V_{cm} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \]

### Step 3: Substitute the values into the formula
Substituting the values we identified:
\[ V_{cm} = \frac{(2 \, \text{kg} \cdot 2 \, \text{m/s}) + (4 \, \text{kg} \cdot -10 \, \text{m/s})}{2 \, \text{kg} + 4 \, \text{kg}} \]

### Step 4: Calculate the numerator and denominator
Calculating the numerator:
\[ = (2 \cdot 2) + (4 \cdot -10) = 4 - 40 = -36 \]
Calculating the denominator:
\[ = 2 + 4 = 6 \]

### Step 5: Calculate the velocity of the center of mass
Now substituting back into the equation:
\[ V_{cm} = \frac{-36}{6} = -6 \, \text{m/s} \]

### Step 6: Interpret the result
The negative sign indicates that the center of mass is moving in the direction of the second body (the 4 kg mass moving left). However, since the question asks for the magnitude of the center of mass velocity, we can say:
\[ |V_{cm}| = 6 \, \text{m/s} \]

### Conclusion
The velocity of the center of mass is \( 6 \, \text{m/s} \) towards the left.