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

Answer

To solve the problem step by step, we can use the formula for the resultant of two forces acting at an angle.

### Step 1: Understand the Given Information
We have two equal forces, let's denote the magnitude of each force as \( F \). The angle between the two forces is \( 60^\circ \), and the resultant force \( R \) is given as \( 40\sqrt{3} \, N \).

### Step 2: Use the Formula for Resultant of Two Forces
The formula for the resultant \( R \) of two forces \( F \) and \( F \) acting 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:
\[ R = \sqrt{2F^2 + 2F^2 \cos(60^\circ)} \]

### Step 3: Substitute the Known Values
We know that \( \cos(60^\circ) = \frac{1}{2} \). Substituting this into the equation gives:
\[ R = \sqrt{2F^2 + 2F^2 \cdot \frac{1}{2}} \]
This simplifies to:
\[ R = \sqrt{2F^2 + F^2} = \sqrt{3F^2} = F\sqrt{3} \]

### Step 4: Set the Resultant Equal to the Given Value
We know that the resultant \( R = 40\sqrt{3} \, N \). Therefore, we can set up the equation:
\[ F\sqrt{3} = 40\sqrt{3} \]

### Step 5: Solve for \( F \)
To find \( F \), we can divide both sides by \( \sqrt{3} \):
\[ F = 40 \, N \]

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