STATEMENT-1 `:` Work done to move a charge on the surface of metal solid charged cylinder is always zero.
and
STATEMENT-2 `:` Work done to move a charge on an equipotential surface is zero.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False , Statement-2 is True

Answer

To solve the given problem, we need to analyze both statements and determine their validity and relationship.

### Step 1: Analyze Statement 1
**Statement 1:** Work done to move a charge on the surface of a metal solid charged cylinder is always zero.

- A charged conductor, such as a metal solid charged cylinder, has an electric field inside it that is equal to zero. This is a fundamental property of conductors in electrostatic equilibrium.
- Since the electric field (E) inside the conductor is zero, the potential (V) across any two points within the conductor is constant. This means that if you move a charge from one point to another on the surface of the conductor, the potential difference (V_A - V_B) is zero.
- The work done (W) in moving a charge (q) between two points is given by the formula:
\[ W = q \cdot (V_A - V_B) \]
- Since \(V_A - V_B = 0\), we have:
\[ W = q \cdot 0 = 0 \]
- Therefore, the work done to move a charge on the surface of a metal solid charged cylinder is indeed zero.

### Step 2: Analyze Statement 2
**Statement 2:** Work done to move a charge on an equipotential surface is zero.

- An equipotential surface is defined as a surface where the electric potential is the same at every point.
- By definition, if the potential difference between any two points on an equipotential surface is zero, then the work done in moving a charge between those two points is also zero.
- This is consistent with the formula for work done:
\[ W = q \cdot (V_A - V_B) \]
- Since \(V_A = V_B\) on an equipotential surface, it follows that:
\[ W = q \cdot 0 = 0 \]
- Thus, the work done to move a charge on an equipotential surface is indeed zero.

### Step 3: Conclusion
- Both statements are true.
- Statement 2 provides the correct explanation for Statement 1, as the surface of a charged conductor behaves as an equipotential surface.

### Final Answer:
- **Statement 1 is true.**
- **Statement 2 is true.**
- **Statement 2 is the correct explanation of Statement 1.**