The resultant of x N force and 5N force is found to be 5N force and perpendicular to the 5N force. Find the angle between the forces. `xN,5N`

Answer

To solve the problem, we need to find the angle between the forces \( x \, \text{N} \) and \( 5 \, \text{N} \) given that their resultant is \( 5 \, \text{N} \) and is perpendicular to the \( 5 \, \text{N} \) force.

### Step-by-Step Solution:

1. **Understand the Forces and Resultant**:
- We have two forces: \( F_1 = x \, \text{N} \) and \( F_2 = 5 \, \text{N} \).
- The resultant \( R \) of these two forces is given as \( R = 5 \, \text{N} \) and is perpendicular to \( F_2 \).

2. **Use the Right Triangle Concept**:
- Since the resultant \( R \) is perpendicular to \( F_2 \), we can visualize this situation as a right triangle where:
- One side is \( F_2 = 5 \, \text{N} \) (the adjacent side).
- The other side is \( F_1 = x \, \text{N} \) (the opposite side).
- The hypotenuse is the resultant \( R = 5 \, \text{N} \).

3. **Apply the Pythagorean Theorem**:
- According to the Pythagorean theorem:
\[ R^2 = F_1^2 + F_2^2 \]
- Substituting the known values:
\[ 5^2 = x^2 + 5^2 \]
- This simplifies to:
\[ 25 = x^2 + 25 \]
- Rearranging gives:
\[ x^2 = 0 \]
- Therefore, \( x = 0 \).

4. **Determine the Angle**:
- The angle \( \theta \) between the forces can be found using trigonometric identities. Since \( F_1 \) is \( 0 \, \text{N} \), it means that the angle between the two forces is \( 90^\circ \) or \( \frac{\pi}{2} \) radians.

### Final Answer:
The angle between the forces \( x \, \text{N} \) and \( 5 \, \text{N} \) is \( 90^\circ \) or \( \frac{\pi}{2} \) radians.

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