Two identical metallic spheres A and B of exactly equal masses are given equal positive and negative charges respectively. Then

Options

A. mass of A `gt` mass of B
B. mass of A `lt` Mass of B
C. mass of A= Mass of B
D. mass of A `le` Mass of B

Answer

To solve the problem step by step, we need to analyze the situation involving the two identical metallic spheres, A and B, which have been given equal but opposite charges.

### Step 1: Understand the Charges
- Sphere A is given a positive charge \( +Q \).
- Sphere B is given a negative charge \( -Q \).

### Step 2: Analyze the Effect of Charges on Mass
- A positive charge indicates that electrons have been removed from Sphere A. This means that the mass of Sphere A decreases because electrons have mass.
- A negative charge indicates that electrons have been added to Sphere B. This means that the mass of Sphere B increases because it now contains additional electrons.

### Step 3: Determine the Change in Mass
- The mass of the electrons that have been removed from Sphere A can be denoted as \( m_e \), where \( m_e \approx 9.11 \times 10^{-31} \) kg (mass of a single electron).
- If \( n \) electrons are removed from Sphere A, the mass of Sphere A decreases by \( n \cdot m_e \).
- Conversely, if \( n \) electrons are added to Sphere B, the mass of Sphere B increases by \( n \cdot m_e \).

### Step 4: Compare the Masses of the Spheres
- Initially, both spheres had equal masses. After the charge transfer:
- Mass of Sphere A = Initial Mass - Mass of Removed Electrons
- Mass of Sphere B = Initial Mass + Mass of Added Electrons
- Since the same number of electrons \( n \) is involved in both cases, we can conclude:
- Mass of Sphere A < Mass of Sphere B

### Conclusion
- Therefore, the mass of Sphere B is greater than the mass of Sphere A.

### Final Answer
- The correct conclusion is that **the mass of Sphere B will be greater than the mass of Sphere A**.

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