Read the given statements and select the correct option.
Statement 1: A man carrying a bucket of water and walking on a rough level road with a uniform velocity does no work while carrying the bucket.
Statement 2 : The work done on a body by a force (F) in giving it a displacement (S) is defined as W= FS cos `theta`, where `theta` is the angle between vectors F and S.

Options

A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1.
C. Statement 1 is true but statement 2 is false.
D. Both statements 1 and 2 are false.

Explanation

To analyze the statements and determine their correctness, we can break down the solution step by step.

### Step 1: Understanding Statement 1
**Statement 1:** A man carrying a bucket of water and walking on a rough level road with a uniform velocity does no work while carrying the bucket.

- **Analysis:**
- Work is defined as the product of force and displacement in the direction of the force. The formula for work done (W) is given by:
\[ W = F \cdot S \cdot \cos(\theta) \]
- Here, \( F \) is the force applied, \( S \) is the displacement, and \( \theta \) is the angle between the force and the direction of displacement.
- In this scenario, the man is carrying the bucket vertically while walking horizontally. The force due to gravity acts downward, while the displacement is horizontal. Therefore, the angle \( \theta \) between the force (weight of the bucket) and the displacement is 90 degrees.
- Since \( \cos(90^\circ) = 0 \), the work done by the man while carrying the bucket is:
\[ W = F \cdot S \cdot \cos(90^\circ) = 0 \]
- Thus, Statement 1 is **true**.

### Step 2: Understanding Statement 2
**Statement 2:** The work done on a body by a force (F) in giving it a displacement (S) is defined as \( W = F \cdot S \cos(\theta) \), where \( \theta \) is the angle between vectors \( F \) and \( S \).

- **Analysis:**
- This statement is a direct representation of the definition of work in physics. It correctly states that the work done is the product of the force applied, the displacement, and the cosine of the angle between the force and displacement vectors.
- Therefore, Statement 2 is also **true**.

### Step 3: Conclusion
Both statements are true, and Statement 2 correctly explains Statement 1.

### Final Answer:
Both Statement 1 and Statement 2 are true, and Statement 2 is the correct explanation of Statement 1.

---