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 analyze the statements provided, we will break down the reasoning step by step.

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

- A metal solid charged cylinder is a conductor. When a conductor is charged, the charge resides on its surface.
- Inside a conductor, the electric field is zero in electrostatic equilibrium. Therefore, any point on the surface of the conductor is at the same electric potential.

**Conclusion for Statement 1:** Since the potential is constant on the surface of the charged cylinder, moving a charge along the surface does not require any work. Thus, Statement 1 is true.

### Step 2: Understanding 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 constant throughout.
- When moving a charge along an equipotential surface, there is no change in potential energy because the potential is the same at all points on that surface.

**Conclusion for Statement 2:** Since there is no change in potential energy when moving a charge on an equipotential surface, the work done is zero. Thus, Statement 2 is also true.

### Step 3: Relationship Between the Two Statements
- The first statement is specifically about the surface of a charged conductor (the metal solid charged cylinder), which is indeed an equipotential surface.
- The second statement provides a general principle about equipotential surfaces.

**Conclusion:** Statement 2 serves as a correct explanation for Statement 1, as it establishes the principle that leads to the conclusion of Statement 1 being true.

### Final Conclusion
Both statements are true, and Statement 2 correctly explains Statement 1.