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 \( 120^\circ \) to each other, we can use the formula for the resultant of two vectors:

\[ R = \sqrt{A^2 + B^2 + 2AB \cos \theta} \]

### Step-by-Step Solution:

1. **Identify the forces and the angle**:
- Let the two equal forces be \( P \) each.
- The angle \( \theta \) between the two forces is \( 120^\circ \).

2. **Substitute the values into the resultant formula**:
- Since both forces are equal, we can substitute \( A = P \) and \( B = P \):
\[ R = \sqrt{P^2 + P^2 + 2 \cdot P \cdot P \cdot \cos(120^\circ)} \]

3. **Simplify the expression**:
- This simplifies to:
\[ R = \sqrt{P^2 + P^2 + 2P^2 \cos(120^\circ)} \]
- Since \( \cos(120^\circ) = -\frac{1}{2} \):
\[ R = \sqrt{P^2 + P^2 + 2P^2 \left(-\frac{1}{2}\right)} \]

4. **Calculate the terms**:
- This becomes:
\[ R = \sqrt{P^2 + P^2 - P^2} \]
- Which simplifies to:
\[ R = \sqrt{P^2} \]

5. **Find the magnitude of the resultant**:
- Therefore, we have:
\[ R = P \]

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

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