Two forces each of magnitude 2N, act at an angle of `60^(@)`. What is the magnitude of the resultant force ?

Options

A. `sqrt(2) N`
B. `sqrt(6) N`
C. `sqrt(8) N`
D. `sqrt(12) N`

Explanation

To find the magnitude of the resultant force when two forces of equal magnitude act at an angle, we can use the law of cosines. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify the Magnitudes and Angle**:
We have two forces, both with a magnitude of \( P = 2 \, \text{N} \) and \( Q = 2 \, \text{N} \), acting at an angle of \( \theta = 60^\circ \).

2. **Use the Formula for Resultant Force**:
The magnitude of the resultant force \( R \) when two forces \( P \) and \( Q \) act at an angle \( \theta \) is given by the formula:
\[ R = \sqrt{P^2 + Q^2 + 2PQ \cos \theta} \]

3. **Substitute the Values**:
Plugging in the values we have:
\[ R = \sqrt{(2)^2 + (2)^2 + 2 \times 2 \times 2 \times \cos(60^\circ)} \]

4. **Calculate Each Term**:
- \( P^2 = 2^2 = 4 \)
- \( Q^2 = 2^2 = 4 \)
- \( \cos(60^\circ) = \frac{1}{2} \)
- Therefore, \( 2PQ \cos(60^\circ) = 2 \times 2 \times 2 \times \frac{1}{2} = 4 \)

5. **Combine the Terms**:
Now, substitute these values back into the equation:
\[ R = \sqrt{4 + 4 + 4} = \sqrt{12} \]

6. **Calculate the Resultant Magnitude**:
Finally, we find the magnitude of the resultant force:
\[ R = \sqrt{12} = 2\sqrt{3} \, \text{N} \]

### Final Answer:
The magnitude of the resultant force is \( R = 2\sqrt{3} \, \text{N} \).