Two charged balls attract each other with a certain force. If they are allowed to touch and then get separated to the same distance apart, the balls will:

Options

A. attract each other with a smaller force
B. attract each other with a greater force
C. repel each other with a smaller force
D. repel each other with a greater force

Explanation

To solve the problem, we need to analyze the situation step by step.

### Step 1: Understanding the Initial Situation
We have two charged balls that attract each other. This means that one ball has a positive charge (let's call it Q1) and the other has a negative charge (let's call it Q2). The force of attraction between them is given by Coulomb's Law:

\[ F = k \frac{|Q1 \cdot Q2|}{r^2} \]

where \( k \) is Coulomb's constant, and \( r \) is the distance between the charges.

### Step 2: Contacting the Balls
When the two charged balls touch, they share their charges. The total charge of the system is conserved. If we assume:

- \( Q1 = +q \)
- \( Q2 = -q \)

Then the total charge when they touch is:

\[ Q_{total} = Q1 + Q2 = q + (-q) = 0 \]

### Step 3: Charge Distribution After Contact
When the balls are brought into contact, they will redistribute their charge evenly. Since the total charge is zero, each ball will end up with a charge of:

\[ Q1' = 0 \quad \text{and} \quad Q2' = 0 \]

### Step 4: Separation of the Balls
After separating the balls, they are now at the same distance \( r \) apart again. Since both balls now have a charge of zero, we can analyze the force between them.

### Step 5: Analyzing the Force After Separation
Now, using Coulomb's Law again, the force between the two balls is:

\[ F' = k \frac{|Q1' \cdot Q2'|}{r^2} = k \frac{|0 \cdot 0|}{r^2} = 0 \]

### Conclusion
After touching and separating, the two balls will not exert any force on each other because they both have zero charge. Therefore, they will neither attract nor repel each other.

### Final Answer
The balls will **not exert any force on each other** after being separated.

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