Statement-I : A cyclist must adopt a zig-zag path while ascending a steep hill.
Statement-II : The zig-zag path prevent the cyclist to slip down.

Options

A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for Statement-I
B. Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for Statement-I
C. Statement-I is true, Statement-II is false
D. Statement-I is false, Statement-II is true.

Answer

To solve the problem, we need to analyze the two statements provided:

**Statement-I**: A cyclist must adopt a zig-zag path while ascending a steep hill.
**Statement-II**: The zig-zag path prevents the cyclist from slipping down.

### Step-by-Step Solution:

1. **Understanding Forces on a Cyclist**:
When a cyclist ascends a steep hill, two main forces act on the cyclist: the gravitational force (mg) acting downward and the force exerted by the cyclist to move upward.

2. **Straight Path Analysis**:
If the cyclist goes straight up the hill, the component of gravitational force acting down the slope is given by \( F = mg \sin \theta \), where \( \theta \) is the angle of the hill with respect to the horizontal. This force tends to pull the cyclist back down.

3. **Zig-Zag Path Analysis**:
If the cyclist adopts a zig-zag path, the angle of ascent changes. Let’s denote the angle of the zig-zag path as \( \alpha \). The component of the gravitational force acting along the zig-zag path can be expressed as \( F' = mg \sin \alpha \).

4. **Comparing Forces**:
In the zig-zag path, the effective force that helps the cyclist ascend is reduced due to the angle \( \alpha \). The force component acting down the slope is now \( F' = mg \sin \alpha \cos \theta \). Since \( \cos \theta < 1 \), it follows that \( F' < mg \sin \theta \).

5. **Conclusion on Slipping**:
Because the effective gravitational force component acting down the zig-zag path is less than that acting down a straight path, the cyclist is less likely to slip down when taking the zig-zag path. Thus, the zig-zag path indeed helps in preventing slipping.

6. **Final Evaluation of Statements**:
- **Statement-I** is true because the zig-zag path is beneficial for ascending steep hills.
- **Statement-II** is also true as it explains why the zig-zag path prevents slipping.

### Final Answer:
Both statements are true, and Statement-II provides a correct explanation for Statement-I.