Two unlike parallel forces 2 N and 16 N act at the ends of a uniform rod of 21 cm length . The point where the resultant of these two act is at a distance of _________ cm from the greater force.

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem of finding the distance from the greater force where the resultant of two unlike parallel forces acts, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces and Their Positions**:
- We have two forces: \( F_1 = 2 \, \text{N} \) (acting at one end of the rod) and \( F_2 = 16 \, \text{N} \) (acting at the other end).
- The length of the rod is \( L = 21 \, \text{cm} \).

2. **Determine the Resultant Force**:
- Since the forces are unlike, the resultant force \( R \) can be calculated as:
\[ R = F_2 - F_1 = 16 \, \text{N} - 2 \, \text{N} = 14 \, \text{N} \]

3. **Set Up the Equation for Moments**:
- Let \( x \) be the distance from the greater force (16 N) to the point where the resultant acts.
- The distance from the smaller force (2 N) to the point where the resultant acts will then be \( 21 - x \).
- According to the principle of moments (taking moments about the point where the 16 N force acts), we have:
\[ \text{Moment due to } 2 \, \text{N} = \text{Moment due to } 14 \, \text{N} \]
\[ 2 \, \text{N} \times (21 - x) = 14 \, \text{N} \times x \]

4. **Simplify the Equation**:
- Expanding the equation gives:
\[ 42 - 2x = 14x \]
- Rearranging the equation results in:
\[ 42 = 14x + 2x \]
\[ 42 = 16x \]

5. **Solve for \( x \)**:
- Dividing both sides by 16 gives:
\[ x = \frac{42}{16} = 2.625 \, \text{cm} \]

6. **Final Calculation**:
- Since we need the distance from the greater force (16 N), we find that:
\[ x \approx 2.625 \, \text{cm} \]

### Conclusion:
The point where the resultant of these two forces acts is approximately **2.625 cm** from the greater force (16 N).