The vectors A , B , C , D represents the forces acting on a body. Which one of the following Fig. 15.14.5. indicates that the body is in equilibrium.

Options

A.
B.
C.
D.

Answer

To determine which configuration of the vectors A, B, C, and D indicates that the body is in equilibrium, we will analyze each option systematically.

### Step-by-Step Solution:

1. **Understanding Equilibrium**:
A body is in equilibrium when the net force acting on it is zero. This means that the vector sum of all forces must equal zero.

2. **Analyzing Option 1**:
- In this option, all vectors A, B, C, and D are acting at a single point.
- For the body to be in equilibrium, the vectors must either be equal in magnitude and opposite in direction or must cancel each other out.
- Since we are not given any information about the magnitudes of A, B, C, and D being equal, we cannot conclude that they cancel each other out.
- **Conclusion**: This option does not indicate equilibrium.

3. **Analyzing Option 2**:
- Here, we will use the parallelogram law of vector addition to find the resultant of A and B.
- Let’s denote the resultant of A and B as R1.
- Next, we find the resultant of B and C, which we denote as R2.
- If R1 and R2 are equal in magnitude and opposite in direction, then the net force will be zero.
- Since the problem states that the magnitudes of the resultant vectors are equal and opposite, we conclude that the net force is zero.
- **Conclusion**: This option indicates that the body is in equilibrium.

4. **Analyzing Option 3**:
- We apply the parallelogram law to find the resultant of A and B, which we denote as R3.
- Then we find the resultant of D and C, denoted as R4.
- If R3 and R4 do not cancel each other out, the net force will not be zero.
- **Conclusion**: This option does not indicate equilibrium.

5. **Analyzing Option 4**:
- Again, we apply the parallelogram law to find the resultant of B and C, denoted as R5.
- We also find the resultant of D and A, denoted as R6.
- If R5 and R6 do not cancel each other out, the net force will not be zero.
- **Conclusion**: This option does not indicate equilibrium.

### Final Answer:
After analyzing all options, we conclude that **Option 2** indicates that the body is in equilibrium.