Two particles of masses 4 kg and 6 kg are at rest separated by 20 m. If they move towards each other under mutual force of attraction, the position of the point where they meet is

Options

A. `12m` from `4kg` body
B. `12m` from `6kg` body
C. `8m` from `4kg` body
D. `10m` from `4kg` body

Answer

To find the position where two particles of masses 4 kg and 6 kg meet when they move towards each other under mutual force of attraction, we can use the concept of the center of mass (COM) of the system. Here's how to solve the problem step by step:

### Step 1: Identify the masses and the distance between them
- Mass of particle 1 (m1) = 4 kg
- Mass of particle 2 (m2) = 6 kg
- Distance between them (d) = 20 m

### Step 2: Set a reference point
- Let's place the 4 kg mass at the origin (0 m).
- Therefore, the position of the 6 kg mass will be at 20 m.

### Step 3: Use the formula for the center of mass
The formula for the center of mass (COM) of a system of particles is given by:
\[ x_{COM} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} \]
where \(x_1\) and \(x_2\) are the positions of the masses.

### Step 4: Substitute the values into the formula
- For the 4 kg mass (m1), \(x_1 = 0\) m.
- For the 6 kg mass (m2), \(x_2 = 20\) m.

Now substituting the values:
\[ x_{COM} = \frac{(4 \, \text{kg} \cdot 0 \, \text{m}) + (6 \, \text{kg} \cdot 20 \, \text{m})}{4 \, \text{kg} + 6 \, \text{kg}} \]
\[ x_{COM} = \frac{0 + 120}{10} = \frac{120}{10} = 12 \, \text{m} \]

### Step 5: Interpret the result
The center of mass is located at 12 m from the 4 kg mass. Since the total distance between the two masses is 20 m, the distance from the 6 kg mass can be calculated as:
\[ \text{Distance from 6 kg} = 20 \, \text{m} - 12 \, \text{m} = 8 \, \text{m} \]

### Conclusion
The two particles will meet at a point that is 12 m from the 4 kg mass and 8 m from the 6 kg mass.

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