The electrostatic potential on the surface of a charged concducting sphere is `100 V`. Two statements are made in this regard
`S_(1) :` at any inside the sphere, electric intensity is zero.
`S_(2) :` at any point inside the sphere, the electrostatic potential is `100 V`.

Options

A. `S_(1)` is true but `S_(2)` is false.
B. Both `S_(1)` and `S_(2)` are false.
C. `S_(1)` is true,`S_(2)` is also true and `S_(1)` is the cause of `S_(2)`.
D. `S_(1)` is true, `S_(2)` is also true but the statements are independent.

Explanation

To solve the question, we need to analyze the two statements regarding the electrostatic potential and electric field inside a charged conducting sphere.

### Step-by-Step Solution:

1. **Understanding the Conducting Sphere**:
- A conducting sphere with a charge will have its charge distributed uniformly on its surface. The electric field inside a conductor in electrostatic equilibrium is zero.

2. **Analyzing Statement S1**:
- **Statement S1**: "At any point inside the sphere, electric intensity is zero."
- According to Gauss's law, the electric field inside a charged conducting sphere is zero because there is no charge enclosed within a Gaussian surface drawn inside the sphere. Therefore, **S1 is true**.

3. **Analyzing Statement S2**:
- **Statement S2**: "At any point inside the sphere, the electrostatic potential is 100 V."
- The potential inside a conductor is constant and equal to the potential on its surface. Since the potential on the surface of the sphere is given as 100 V, the potential at any point inside the sphere must also be 100 V. Therefore, **S2 is also true**.

4. **Conclusion**:
- Both statements S1 and S2 are correct. S1 is true because the electric field inside the sphere is zero, and S2 is true because the potential remains constant throughout the conducting sphere and is equal to the surface potential.

### Final Answer:
Both statements S1 and S2 are true.