Four point positive charges are held at the vertices of a square in a horizontal plane. Their masses are `1kg, 2kg, 3kg, & 4kg`. Another point positive charge of mass `10 kg` is kept on the axis of the sqaure. The weight of their fifth charge is balanced by the electrostatic force due to those four charges. If the four charge on the vertices are released such that they can freely move in any direction(vertical, horizontal etc.) then the acceleration of the centres of mass of the four charges immediately after the release is (Use `g= 10m//s^(2)`)

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript while ensuring clarity and completeness in our explanation.

### Step 1: Understand the System
We have four point positive charges located at the vertices of a square and a fifth charge of mass 10 kg placed on the axis of the square. The four charges have masses of 1 kg, 2 kg, 3 kg, and 4 kg. The weight of the fifth charge is balanced by the electrostatic force due to the four charges.

### Step 2: Calculate the Weight of the Fifth Charge
The weight of the fifth charge (mass = 10 kg) can be calculated using the formula:
\[ W = mg \]
Where \( g = 10 \, \text{m/s}^2 \).
\[ W = 10 \, \text{kg} \times 10 \, \text{m/s}^2 = 100 \, \text{N} \]

### Step 3: Determine the Electrostatic Force
Since the weight of the fifth charge is balanced by the electrostatic force (Fe) from the four charges, we have:
\[ Fe = W = 100 \, \text{N} \]

### Step 4: Calculate the Total Force Acting on the System
When the four charges are released, they will experience a net force due to their mutual repulsion. The total force acting on the center of mass of the four charges can be considered as the sum of their individual forces. Since they are all positive charges, they will repel each other.

The total force acting on the system will be:
\[ F_{\text{total}} = Fe + W = 100 \, \text{N} + 100 \, \text{N} = 200 \, \text{N} \]

### Step 5: Calculate the Total Mass of the Four Charges
The total mass of the four charges is:
\[ m_{\text{total}} = 1 \, \text{kg} + 2 \, \text{kg} + 3 \, \text{kg} + 4 \, \text{kg} = 10 \, \text{kg} \]

### Step 6: Calculate the Acceleration of the Center of Mass
Using Newton's second law, we can find the acceleration (a) of the center of mass of the four charges:
\[ a = \frac{F_{\text{total}}}{m_{\text{total}}} \]
Substituting the values:
\[ a = \frac{200 \, \text{N}}{10 \, \text{kg}} = 20 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the center of mass of the four charges immediately after the release is:
\[ \boxed{20 \, \text{m/s}^2} \]

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