The resultant of two forces cannot exceed

Options

A. average of the forces
B. algebraic sum of the two forces
C. difference of the two forces
D. none

Answer

To solve the question "The resultant of two forces cannot exceed", we will analyze the options given and apply the principles of vector addition.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to determine the maximum possible value of the resultant force when two forces are acting. Forces are vector quantities, which means they have both magnitude and direction.

2. **Identify the Options**:
The options provided are:
- A) Average of the forces
- B) Algebraic sum of the two forces
- C) Difference of the two forces
- D) Null (zero)

3. **Vector Addition Principles**:
The resultant force of two vectors can be calculated using vector addition laws. The maximum resultant occurs when the two forces are in the same direction, and the minimum resultant occurs when they are in opposite directions.

4. **Using the Triangle Law of Vector Addition**:
According to the triangle law of vector addition, if two vectors are represented as two sides of a triangle, the resultant vector can be represented by the third side of the triangle.

5. **Using the Parallelogram Law of Vector Addition**:
The parallelogram law states that if two vectors are represented in magnitude and direction by the two adjacent sides of a parallelogram, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram.

6. **Calculating Maximum Resultant**:
If we denote the two forces as \( P \) and \( Q \), the maximum resultant \( R \) can be given by:
\[ R_{\text{max}} = P + Q \]
This occurs when the two forces are acting in the same direction.

7. **Calculating Minimum Resultant**:
The minimum resultant occurs when the two forces are acting in opposite directions:
\[ R_{\text{min}} = |P - Q| \]

8. **Conclusion**:
The resultant of two forces cannot exceed the algebraic sum of the two forces when they are acting in the same direction. Therefore, the correct answer is:
\[ \text{Option B: Algebraic sum of the two forces} \]