Two forces having magnitube `A` and `A/2` are perpendicular to each other. The magnitube of their resultant is:

Options

A. `(sqrt5A)/2`
B. `(sqrt5A^(2))/2`
C. `(5A)/2`
D. `(sqrt5A)/4`

Answer

To solve the problem of finding the magnitude of the resultant of two forces that are perpendicular to each other, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces**:
We have two forces with magnitudes \( A \) and \( \frac{A}{2} \).

2. **Understanding Perpendicular Forces**:
Since the forces are perpendicular, we can represent them as vectors at right angles to each other.

3. **Using the Pythagorean Theorem**:
The magnitude of the resultant force \( F \) can be calculated using the Pythagorean theorem:
\[ F = \sqrt{(A)^2 + \left(\frac{A}{2}\right)^2} \]

4. **Calculating the Squares**:
Calculate \( (A)^2 \) and \( \left(\frac{A}{2}\right)^2 \):
\[ (A)^2 = A^2 \]
\[ \left(\frac{A}{2}\right)^2 = \frac{A^2}{4} \]

5. **Adding the Squares**:
Now, add the two results:
\[ F = \sqrt{A^2 + \frac{A^2}{4}} = \sqrt{A^2 + 0.25A^2} = \sqrt{1.25A^2} \]

6. **Factor out \( A^2 \)**:
This can be simplified as:
\[ F = \sqrt{\frac{5A^2}{4}} = \sqrt{5} \cdot \frac{A}{2} \]

7. **Final Result**:
Therefore, the magnitude of the resultant force is:
\[ F = \frac{A \sqrt{5}}{2} \]

### Conclusion:
The magnitude of the resultant of the two forces is \( \frac{A \sqrt{5}}{2} \).

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