STATEEMNT-1 `:` Work done by frictional force is always either negative or zero.
because
STATEMENT-2 `:` Work done by the static friction on a system may be zero.

Answer

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

### Step 1: Understanding Statement 1
**Statement 1:** "Work done by frictional force is always either negative or zero."

- The work done by a force is calculated using the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \( W \) is the work done, \( F \) is the force, \( d \) is the displacement, and \( \theta \) is the angle between the force and the displacement vector.

- For frictional force, it always acts opposite to the direction of motion. Therefore, the angle \( \theta \) between the frictional force and displacement is 180 degrees (or \( \pi \) radians), making \( \cos(180^\circ) = -1 \).

- This means that the work done by kinetic friction is negative:
\[ W = F_{\text{friction}} \cdot d \cdot (-1) = -F_{\text{friction}} \cdot d \]

- The work done can also be zero if there is no displacement (e.g., if an object is at rest and not moving). Thus, statement 1 is incorrect because work done by friction can be positive in certain scenarios, such as when static friction prevents slipping.

### Step 2: Understanding Statement 2
**Statement 2:** "Work done by the static friction on a system may be zero."

- Static friction acts to prevent motion between surfaces. If an object is stationary and a force is applied that does not exceed the maximum static friction, the object does not move.

- In this case, since there is no displacement (\( d = 0 \)), the work done by static friction is:
\[ W = F_{\text{static}} \cdot 0 = 0 \]

- Therefore, statement 2 is correct because static friction can indeed do zero work when there is no movement.

### Conclusion
- **Statement 1** is **false** because work done by friction can be positive in certain conditions.
- **Statement 2** is **true** because static friction can do zero work when there is no displacement.

### Final Answer
- Statement 1 is false, and Statement 2 is true. The correct option is D (Statement 1 is false, Statement 2 is true).

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