Two equal forces are acting at a point with an angle `60^(@)` between them. If the resultant force is equal to `4sqrt(3)N`, the magnitude of each force is

Options

A. 4 N
B. 2 N
C. 8 N
D. 3 N

Explanation

To solve the problem, we need to find the magnitude of each force when two equal forces are acting at a point with an angle of 60 degrees between them, and the resultant force is given as \(4\sqrt{3} \, \text{N}\).

### Step-by-Step Solution:

1. **Understand the Problem**: We have two equal forces \(F\) acting at an angle of \(60^\circ\). We need to find the magnitude of each force given that the resultant force \(R\) is \(4\sqrt{3} \, \text{N}\).

2. **Use the Formula for Resultant of Two Forces**: The formula for the resultant \(R\) of two forces \(F\) at an angle \(\theta\) is given by:
\[ R = \sqrt{F^2 + F^2 + 2FF \cos(\theta)} \]
Since the forces are equal, we can simplify this to:
\[ R = \sqrt{2F^2(1 + \cos(\theta))} \]

3. **Substitute the Angle**: Here, \(\theta = 60^\circ\). We know that \(\cos(60^\circ) = \frac{1}{2}\). Substituting this into the equation gives:
\[ R = \sqrt{2F^2\left(1 + \frac{1}{2}\right)} = \sqrt{2F^2 \cdot \frac{3}{2}} = \sqrt{3F^2} = F\sqrt{3} \]

4. **Set the Resultant Equal to Given Value**: We know that the resultant \(R\) is \(4\sqrt{3} \, \text{N}\). Therefore, we can set up the equation:
\[ F\sqrt{3} = 4\sqrt{3} \]

5. **Solve for \(F\)**: To isolate \(F\), divide both sides by \(\sqrt{3}\):
\[ F = 4 \]

6. **Conclusion**: The magnitude of each force is \(4 \, \text{N}\).

### Final Answer:
The magnitude of each force is \(4 \, \text{N}\).