One metallic sphere `A` is given positive charge whereas another identical metallic sphere `B` of exactly same mass as of `A` is given equal amount of negative charge. Then

Options

A. mass of A and mass of B still remain equal
B. mass of A increase
C. mass of B decrease
D. mass of B increase

Answer

To solve the problem, we need to analyze the situation involving the two metallic spheres A and B, which are charged differently.

### Step-by-Step Solution:

1. **Understanding the Charges**:
- Sphere A is given a positive charge. This means that electrons are removed from sphere A, leading to a deficiency of negative charge (electrons).
- Sphere B is given an equal amount of negative charge. This means that electrons are added to sphere B.

2. **Mass of the Spheres**:
- Initially, both spheres A and B have the same mass. Let's denote the mass of each sphere as \( m \).

3. **Effect of Charge on Mass**:
- When electrons are removed from sphere A to create a positive charge, the mass of sphere A decreases slightly because electrons have mass (though very small).
- Conversely, when electrons are added to sphere B to create a negative charge, the mass of sphere B increases slightly.

4. **Comparing the Masses**:
- After charging, the mass of sphere A will be \( m - \Delta m \) (where \( \Delta m \) is the mass of the electrons removed).
- The mass of sphere B will be \( m + \Delta m \) (where \( \Delta m \) is the mass of the electrons added).

5. **Conclusion**:
- Since sphere A loses mass and sphere B gains mass, the mass of sphere B increases compared to the mass of sphere A. Therefore, the correct conclusion is that the mass of sphere B increases.

### Final Answer:
The mass of sphere B increases.

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