Two like parallel force 20 N and 30 N act at the ands A and B of a rod 1.5 m long. The resultant of the forces will act at the point

Options

A. 90 cm from A
B. 75 cm from B
C. 20 cm from B
D. 85 cm from A

Answer

To solve the problem, we need to find the point where the resultant of the two parallel forces (20 N and 30 N) acts on a rod of length 1.5 m.

### Step-by-step Solution:

1. **Identify the Forces and Their Positions**:
- We have two forces:
- \( F_1 = 20 \, \text{N} \) acting at point A (left end of the rod).
- \( F_2 = 30 \, \text{N} \) acting at point B (right end of the rod).
- The length of the rod is \( L = 1.5 \, \text{m} \).

2. **Calculate the Resultant Force**:
- The resultant force \( R \) is the sum of the two forces:
\[ R = F_1 + F_2 = 20 \, \text{N} + 30 \, \text{N} = 50 \, \text{N} \]

3. **Determine the Torque About Point A**:
- The torque due to a force is given by the formula:
\[ \text{Torque} = \text{Force} \times \text{Perpendicular Distance} \]
- The torque due to the 30 N force about point A is:
\[ \tau_{F_2} = F_2 \times L = 30 \, \text{N} \times 1.5 \, \text{m} = 45 \, \text{N m} \]
- The torque due to the 20 N force about point A is zero since it acts at point A.

4. **Set Up the Equation for the Resultant Torque**:
- Let \( x \) be the distance from point A where the resultant force acts. The torque due to the resultant force about point A is:
\[ \tau_R = R \times x = 50 \, \text{N} \times x \]

5. **Equate the Torques**:
- Since the torques must be equal for the system to be in equilibrium, we have:
\[ \tau_{F_2} = \tau_R \]
\[ 45 \, \text{N m} = 50 \, \text{N} \times x \]

6. **Solve for \( x \)**:
- Rearranging the equation gives:
\[ x = \frac{45 \, \text{N m}}{50 \, \text{N}} = 0.9 \, \text{m} = 90 \, \text{cm} \]

7. **Determine the Distance from Point B**:
- The distance from point B to the point where the resultant acts is:
\[ L - x = 1.5 \, \text{m} - 0.9 \, \text{m} = 0.6 \, \text{m} = 60 \, \text{cm} \]

### Conclusion:
The resultant of the forces will act at a point 90 cm from point A (or 60 cm from point B).