Two equal forces are acting at a point with an angle of `60^(@)` between them. If the resultant force is equal to `40sqrt3` N, the magnitude of each force is

Options

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

Answer

To solve the problem, we need to find the magnitude of each of the two equal forces acting at an angle of 60 degrees, given that the resultant force is \( 40\sqrt{3} \) N.

### Step-by-Step Solution:

1. **Understanding the Forces**:
Let the magnitude of each force be \( F \). Since the forces are equal, we have two forces \( F \) acting at an angle of \( 60^\circ \) between them.

2. **Using the Resultant Force Formula**:
The formula for the resultant \( R \) of two vectors \( A \) and \( B \) at an angle \( \theta \) is given by:
\[ R = \sqrt{A^2 + B^2 + 2AB \cos(\theta)} \]
In our case, both forces are equal, so \( A = B = F \) and \( \theta = 60^\circ \). Thus, the formula becomes:
\[ R = \sqrt{F^2 + F^2 + 2F \cdot F \cos(60^\circ)} \]

3. **Substituting Values**:
We know that \( \cos(60^\circ) = \frac{1}{2} \). Therefore, we can substitute this value into the equation:
\[ R = \sqrt{F^2 + F^2 + 2F^2 \cdot \frac{1}{2}} \]
Simplifying this gives:
\[ R = \sqrt{F^2 + F^2 + F^2} = \sqrt{3F^2} = F\sqrt{3} \]

4. **Setting Up the Equation**:
We are given that the resultant force \( R = 40\sqrt{3} \) N. Therefore, we can set up the equation:
\[ F\sqrt{3} = 40\sqrt{3} \]

5. **Solving for \( F \)**:
To find \( F \), we can divide both sides of the equation by \( \sqrt{3} \):
\[ F = 40 \text{ N} \]

### Conclusion:
The magnitude of each force is \( 40 \) N.