The resultant force of 5 N and 10 N cannot be

Options

A. 12 N
B. 8 N
C. 4 N
D. 5 N

Answer

To find the resultant force of two vectors, we can use the triangle law of vector addition. Given two forces of magnitudes 5 N and 10 N, we can determine the possible values for their resultant force.

### Step-by-Step Solution:

1. **Understanding Vector Addition**:
The resultant of two vectors can be calculated using the formula:
\[ R = \sqrt{A^2 + B^2 + 2AB \cos \theta} \]
where \( A \) and \( B \) are the magnitudes of the vectors, and \( \theta \) is the angle between them.

2. **Finding Maximum Resultant**:
The maximum resultant occurs when the two vectors are in the same direction (i.e., \( \theta = 0^\circ \)):
\[ R_{\text{max}} = A + B = 5 \, \text{N} + 10 \, \text{N} = 15 \, \text{N} \]

3. **Finding Minimum Resultant**:
The minimum resultant occurs when the two vectors are in opposite directions (i.e., \( \theta = 180^\circ \)):
\[ R_{\text{min}} = |A - B| = |5 \, \text{N} - 10 \, \text{N}| = 5 \, \text{N} \]

4. **Determining Possible Resultant Values**:
Therefore, the resultant force \( R \) can take any value between the minimum and maximum:
\[ 5 \, \text{N} \leq R \leq 15 \, \text{N} \]

5. **Conclusion**:
The resultant force cannot be less than 5 N or greater than 15 N. Thus, any value outside this range is not possible.

Therefore, the resultant force of 5 N and 10 N cannot be **12 N** (as it is within the range), **8 N** (as it is within the range), or **4 N** (as it is outside the range).

### Final Answer:
The resultant force of 5 N and 10 N cannot be **4 N**.