Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.
Reason R : Capacitance of metallic spheres depend on the radii of spheres.
In the light of the above statements, choose the correct answer from the options given below

Options

A. Both `A `and` R `are true and` R `is the correct explanation of `A`
B. Both `A `and `R` are true but `R` is not the correct explanation of `A`
C. `A` is true but `R` is false
D. `A `is false but `R `is true

Answer

To solve the problem, we need to analyze both the Assertion (A) and the Reason (R) provided in the question.

### Step 1: Analyze the Assertion (A)
The assertion states: "Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. The solid sphere will have lower charge than the hollow one."

- **Understanding the Assertion**:
- Both spheres are charged to the same potential (V).
- The charge (Q) on a conductor is given by the formula:
\[ Q = C \cdot V \]
- Where \( C \) is the capacitance of the sphere.

### Step 2: Capacitance of Spheres
- The capacitance \( C \) of a metallic sphere is given by:
\[ C = 4\pi \epsilon_0 r \]
where \( r \) is the radius of the sphere and \( \epsilon_0 \) is the permittivity of free space.

### Step 3: Compare the Charges
- Since both spheres have the same radius and are charged to the same potential, we can conclude:
- The capacitance of both spheres will be the same because they have the same radius.
- Therefore, the charges on both spheres will also be the same when charged to the same potential.

### Conclusion for Assertion (A)
- The assertion that the solid sphere will have lower charge than the hollow one is **false**. Both spheres will have the same charge.

### Step 4: Analyze the Reason (R)
The reason states: "Capacitance of metallic spheres depends on the radii of spheres."

- This statement is **true**. The capacitance of a metallic sphere is directly proportional to its radius.

### Final Evaluation
- Assertion (A) is **false**.
- Reason (R) is **true**.

### Answer
Based on the analysis:
- The correct answer is that Assertion A is false and Reason R is true.