The resultant of two equal forces is 141.4N when they are mutually perpendicular. When they are inclined at an angle 120°, then the resultant force will be

Options

A. 100 N
B. 141.4N
C. 196 N
D. Zero

Answer

To find the resultant force when two equal forces are inclined at an angle of 120°, we can follow these steps:

### Step 1: Understand the Given Information
We know that the resultant of two equal forces is 141.4 N when they are mutually perpendicular. Let's denote the magnitude of each force as \( F \).

### Step 2: Use the Resultant Formula for Perpendicular Forces
When two forces \( F \) are perpendicular, the resultant \( R \) can be calculated using the formula:
\[ R = \sqrt{F^2 + F^2} = \sqrt{2F^2} = F\sqrt{2} \]
Given that \( R = 141.4 \, \text{N} \), we can set up the equation:
\[ F\sqrt{2} = 141.4 \]

### Step 3: Solve for \( F \)
To find \( F \), we rearrange the equation:
\[ F = \frac{141.4}{\sqrt{2}} = \frac{141.4}{1.414} \approx 100 \, \text{N} \]

### Step 4: Calculate the Resultant for Forces at 120°
Now, we need to find the resultant when the two forces are inclined at an angle of 120°. The formula for the resultant \( R \) when two forces \( F \) are inclined at an angle \( \theta \) is:
\[ R = \sqrt{F^2 + F^2 + 2F \cdot F \cdot \cos(\theta)} \]
Substituting \( \theta = 120^\circ \):
\[ R = \sqrt{F^2 + F^2 + 2F^2 \cos(120^\circ)} \]

### Step 5: Substitute the Values
Since \( \cos(120^\circ) = -\frac{1}{2} \):
\[ R = \sqrt{F^2 + F^2 + 2F^2 \left(-\frac{1}{2}\right)} \]
This simplifies to:
\[ R = \sqrt{F^2 + F^2 - F^2} = \sqrt{F^2} = F \]

### Step 6: Final Result
Since we found \( F \approx 100 \, \text{N} \), the resultant when the forces are inclined at 120° is:
\[ R = 100 \, \text{N} \]

### Conclusion
The resultant force when the two equal forces are inclined at an angle of 120° is **100 N**.

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