Assertion : A and B are two conducting spheres of same radius. A being solid and B hollow. Both are charged to the same potential. Then, charge on A= charge on B.
Reason : Potentials on both are same.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the question, we need to analyze the assertion and reason provided.

**Assertion:** A and B are two conducting spheres of the same radius. A is solid and B is hollow. Both are charged to the same potential. Then, charge on A = charge on B.

**Reason:** Potentials on both are the same.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- We have two conducting spheres, A (solid) and B (hollow), both with the same radius.
- Both spheres are charged to the same potential.

2. **Formula for Electric Potential:**
- The electric potential \( V \) at the surface of a conducting sphere is given by the formula:
\[ V = \frac{kQ}{R} \]
where \( k \) is Coulomb's constant, \( Q \) is the charge, and \( R \) is the radius of the sphere.

3. **Applying the Formula:**
- For sphere A (solid):
\[ V_A = \frac{kQ_A}{R} \]
- For sphere B (hollow):
\[ V_B = \frac{kQ_B}{R} \]

4. **Setting the Potentials Equal:**
- Since both spheres are charged to the same potential, we can equate the potentials:
\[ V_A = V_B \]
This gives us:
\[ \frac{kQ_A}{R} = \frac{kQ_B}{R} \]

5. **Simplifying the Equation:**
- The \( k \) and \( R \) terms cancel out (since they are the same for both spheres):
\[ Q_A = Q_B \]

6. **Conclusion:**
- Therefore, the charge on sphere A is equal to the charge on sphere B, confirming the assertion.

### Evaluation of the Reason:
- The reason states that the potentials on both are the same. While this is true, it does not explain why the charges must be equal. The equality of charges arises from the relationship between charge and potential, but the reason does not directly address this relationship. Thus, while both the assertion and reason are true, the reason is not a correct explanation for the assertion.

### Final Answer:
- The assertion is true, but the reason is not a correct explanation for the assertion. Therefore, the correct option is B.

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