Statement-1 : A hollow metallic sphere of inner radius a and outer radius b has charge q at the centre. A negatively charged moves from inner surface outer surface. Then total work done will be zero.
Statement-2: Potential is constant inside the metallic sphere.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation of statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation of statement -1
C. Statement-1 is False, Statement-2 is True
D. Statement-1 is True, Statement-2 is False.

Answer

To solve the question, we need to analyze the two statements provided regarding a hollow metallic sphere with a charge at its center.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a hollow metallic sphere with an inner radius \( a \) and an outer radius \( b \).
- There is a charge \( q \) located at the center of the sphere.
- A negatively charged particle is moving from the inner surface of the sphere to the outer surface.

2. **Electric Field Inside the Metallic Sphere**:
- In electrostatics, the electric field inside a conductor in electrostatic equilibrium is zero.
- Since the sphere is metallic, the electric field \( E \) inside the hollow part (between the inner surface and outer surface) is zero.

3. **Force on the Negatively Charged Particle**:
- The force \( F \) acting on a charge \( q' \) in an electric field \( E \) is given by \( F = q' E \).
- Since \( E = 0 \) inside the hollow region, the force acting on the negatively charged particle is also zero: \( F = q' \cdot 0 = 0 \).

4. **Work Done by the Electric Field**:
- The work done \( W \) by the electric field when moving a charge from point A to point B is given by the integral of the force along the path:
\[ W = \int_{A}^{B} F \cdot dr \]
- Since the force \( F = 0 \), the work done is:
\[ W = 0 \]

5. **Analyzing Statement 1**:
- Statement 1 claims that the total work done when the negatively charged particle moves from the inner surface to the outer surface is zero.
- Based on our analysis, this statement is **correct**.

6. **Analyzing Statement 2**:
- Statement 2 claims that the potential is constant inside the metallic sphere.
- Since the electric field \( E \) is zero in the hollow region, the potential \( V \) must be constant throughout that region.
- However, this statement can be misleading because the potential outside the sphere can vary depending on the distance from the center. But within the hollow region, the potential remains constant.
- Therefore, this statement is also **correct**.

7. **Conclusion**:
- Since both statements are correct, we conclude that the total work done is zero, and the potential is constant inside the metallic sphere.

### Final Answer:
- Statement 1 is true, and Statement 2 is true.