Two equal forces are acting at a point with an angle of `60^(@)` between them. If the resultant force is equal to `40sqrt(3)N`, The magnitude of each force is :-

Options

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

Answer

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 \(60^\circ\) between them, and the resultant force is given as \(40\sqrt{3} \, N\).

### Step-by-Step Solution:

1. **Identify the Forces and Angle**:
Let the magnitude of each force be \(F\). The angle between the two forces is given as \(60^\circ\).

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

3. **Substitute the Value of \(\cos(60^\circ)\)**:
We know that \(\cos(60^\circ) = \frac{1}{2}\). Substituting this value into the equation gives:
\[ R = \sqrt{2F^2 + 2F^2 \cdot \frac{1}{2}} = \sqrt{2F^2 + F^2} = \sqrt{3F^2} \]

4. **Express the Resultant in Terms of \(F\)**:
Therefore, we can write:
\[ R = \sqrt{3}F \]

5. **Set the Resultant Equal to the Given Value**:
We are given that the resultant \(R = 40\sqrt{3} \, N\). So, we set up the equation:
\[ \sqrt{3}F = 40\sqrt{3} \]

6. **Solve for \(F\)**:
To find \(F\), we can divide both sides by \(\sqrt{3}\):
\[ F = 40 \]

7. **Conclusion**:
The magnitude of each force is \(40 \, N\).

### Final Answer:
The magnitude of each force is \(40 \, N\).