Two equal forces (P each) act at a point inclined to each other at an angle of `120^(@)`. The magnitude of their resultant is

Options

A. `(P)/(2)`
B. `(P)/(4)`
C. P
D. 2P

Explanation

To find the magnitude of the resultant of two equal forces \( P \) acting at an angle of \( 120^\circ \), we can use the formula for the resultant of two vectors:

\[ R = \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos \theta} \]

### Step-by-Step Solution

1. **Identify the Forces**:
Given that both forces are equal, we have:
\[ F_1 = P \quad \text{and} \quad F_2 = P \]

2. **Angle Between Forces**:
The angle \( \theta \) between the two forces is given as:
\[ \theta = 120^\circ \]

3. **Substituting Values into the Formula**:
Substitute \( F_1 \), \( F_2 \), and \( \theta \) into the resultant formula:
\[ R = \sqrt{P^2 + P^2 + 2 \cdot P \cdot P \cdot \cos(120^\circ)} \]

4. **Calculate \( \cos(120^\circ) \)**:
The cosine of \( 120^\circ \) is:
\[ \cos(120^\circ) = -\frac{1}{2} \]

5. **Substituting \( \cos(120^\circ) \)**:
Now substitute \( \cos(120^\circ) \) into the equation:
\[ R = \sqrt{P^2 + P^2 + 2 \cdot P \cdot P \cdot \left(-\frac{1}{2}\right)} \]

6. **Simplifying the Expression**:
This simplifies to:
\[ R = \sqrt{P^2 + P^2 - P^2} = \sqrt{P^2} \]

7. **Final Result**:
Therefore, the magnitude of the resultant force is:
\[ R = P \]

### Conclusion
The magnitude of the resultant of the two equal forces \( P \) acting at an angle of \( 120^\circ \) is \( P \).