Two equal forces are acting at a point with an angle of 60° between them. If the resultant force is equal to `30sqrt(3)` N, the magnitude of each force is 

Options

A. 40N
B. 20N
C. 80N
D. 30N

Explanation

To solve the problem, we need to find the magnitude of each of the two equal forces acting at a point with an angle of 60° between them, given that the resultant force is equal to \(30\sqrt{3}\) N.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Let the magnitude of each force be \( P \).
- The angle between the two forces, \( \theta = 60^\circ \).
- The magnitude of the resultant force, \( R = 30\sqrt{3} \) N.

2. **Use the Formula for Resultant of Two Forces:**
The formula for the resultant \( R \) of two forces \( P \) and \( P \) acting at an angle \( \theta \) is given by:
\[ R = \sqrt{P^2 + P^2 + 2P \cdot P \cdot \cos(\theta)} \]
Since both forces are equal, we can simplify this to:
\[ R = \sqrt{2P^2 + 2P^2 \cos(60^\circ)} \]

3. **Substitute the Values:**
We know that \( \cos(60^\circ) = \frac{1}{2} \). Therefore, substituting this value into the equation gives:
\[ R = \sqrt{2P^2 + 2P^2 \cdot \frac{1}{2}} \]
This simplifies to:
\[ R = \sqrt{2P^2 + P^2} = \sqrt{3P^2} \]

4. **Express the Resultant in Terms of P:**
Thus, we can express the resultant as:
\[ R = \sqrt{3}P \]

5. **Set Up the Equation:**
Now we equate this expression to the given resultant:
\[ \sqrt{3}P = 30\sqrt{3} \]

6. **Solve for P:**
To find \( P \), divide both sides by \( \sqrt{3} \):
\[ P = 30 \]

### Conclusion:
The magnitude of each force is \( 30 \) N.