Theresultant of two like parallel forces is 12 N. The distance between the forces is 18 metres. If one force is of 4 N, then the distance of the resultant from the smaller force is

Options

A. 4 m
B. 8 m
C. 12 m
D. None of these

Answer

To solve the problem, we need to find the distance of the resultant force from the smaller force (4 N). We can use the principle of moments (torque) to balance the forces.

### Step-by-Step Solution:

1. **Identify the Forces**:
- Let \( F_1 = 4 \, \text{N} \) (the smaller force).
- Let \( F_2 = 12 \, \text{N} - 4 \, \text{N} = 8 \, \text{N} \) (the larger force).
- The distance between the two forces is given as \( d = 18 \, \text{m} \).

2. **Set Up the Moment Equation**:
- The moment (torque) about the point where the smaller force (4 N) acts can be calculated.
- Let \( x \) be the distance from the smaller force (4 N) to the resultant force (R).
- The distance from the larger force (8 N) to the resultant force will then be \( 18 - x \).

3. **Calculate the Moment**:
- The moment due to the smaller force (4 N) about the point where it acts is:
\[ \text{Moment}_{4N} = 4 \cdot x \]
- The moment due to the larger force (8 N) about the same point is:
\[ \text{Moment}_{8N} = 8 \cdot (18 - x) \]

4. **Set the Moments Equal**:
- Since the system is in equilibrium, the clockwise moments must equal the anticlockwise moments:
\[ 4x = 8(18 - x) \]

5. **Solve for x**:
- Expanding the equation:
\[ 4x = 144 - 8x \]
- Combine like terms:
\[ 4x + 8x = 144 \]
\[ 12x = 144 \]
- Divide both sides by 12:
\[ x = 12 \, \text{m} \]

6. **Conclusion**:
- The distance of the resultant force from the smaller force (4 N) is \( 12 \, \text{m} \).