Work done upon a body is

Options

A. a vector quantity
B. a scalar quantity
C. always positive
D. always negative

Explanation

To solve the question "Work done upon a body is," we need to analyze the definition and characteristics of work done in physics. Let's break it down step by step:

### Step 1: Understanding Work Done
Work done (W) on a body is defined as the product of the force (F) applied to the body and the displacement (S) of the body in the direction of the force. Mathematically, it can be expressed as:

\[ W = F \cdot S \cdot \cos(\theta) \]

where:
- \( W \) is the work done,
- \( F \) is the magnitude of the force applied,
- \( S \) is the displacement of the body,
- \( \theta \) is the angle between the force and the displacement vector.

### Step 2: Work Done as a Scalar Quantity
Work done is a scalar quantity, meaning it has magnitude but no direction. This is important to note because it distinguishes work from vector quantities like force and displacement.

### Step 3: Conditions for Work Done
1. **Positive Work**: Work is done positively when the force and displacement are in the same direction. For example, if a force is applied in the direction of the displacement, \( \theta = 0^\circ \) and \( \cos(0) = 1 \), thus:

\[ W = F \cdot S \cdot 1 = F \cdot S \]

2. **Negative Work**: Work is done negatively when the force and displacement are in opposite directions. For instance, if the force is applied in the opposite direction to the displacement, \( \theta = 180^\circ \) and \( \cos(180) = -1 \), thus:

\[ W = F \cdot S \cdot (-1) = -F \cdot S \]

3. **Zero Work**: Work is zero when the force is perpendicular to the displacement. In this case, \( \theta = 90^\circ \) and \( \cos(90) = 0 \), thus:

\[ W = F \cdot S \cdot 0 = 0 \]

### Step 4: Conclusion
From the analysis, we conclude that work done can be:
- Positive when force and displacement are in the same direction.
- Negative when force and displacement are in opposite directions.
- Zero when force is perpendicular to displacement.

Thus, the answer to the question "Work done upon a body is" can be summarized as follows:
- Work done is a scalar quantity.
- It can be positive, negative, or zero depending on the direction of force relative to displacement.