Two copper spheres of the same radii one hollow and the other solid are charged to same potential then

Options

A. Sphere x will have more charge
B. Sphere y will have more charge
C. Charge on both the spheres are equal
D. Charges on both the sphere are zero

Answer

To solve the problem, we need to analyze the situation involving two copper spheres (one hollow and one solid) that are charged to the same potential.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have two copper spheres of the same radius: one is hollow (let's call it Sphere X) and the other is solid (let's call it Sphere Y). Both spheres are charged to the same electric potential.

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

3. **Setting Up the Equations**:
Let \( Q_1 \) be the charge on the hollow sphere (Sphere X) and \( Q_2 \) be the charge on the solid sphere (Sphere Y). Since both spheres are at the same potential, we can write:
\[ V_1 = V_2 \]
This leads to:
\[ \frac{kQ_1}{R} = \frac{kQ_2}{R} \]

4. **Simplifying the Equation**:
We can cancel \( k \) and \( R \) from both sides of the equation (since they are constants and the same for both spheres):
\[ Q_1 = Q_2 \]

5. **Conclusion**:
This shows that the charge on both spheres must be equal. Therefore, the correct answer to the question is that the charges on both spheres are equal.

### Final Answer:
The charges on both the hollow and solid spheres are equal.