Two forces P and Q are acting on the same body. If `P=(25+-0.2)N` and `Q=(16+-0.7)N` find their resultant when the two forces are (i) in the same direction and (ii) in opposite direction.

Answer

To solve the problem of finding the resultant of two forces \( P \) and \( Q \) acting on the same body, we will consider two scenarios: when the forces are in the same direction and when they are in opposite directions.

### Given:
- \( P = 25 \pm 0.2 \, \text{N} \)
- \( Q = 16 \pm 0.7 \, \text{N} \)

### (i) When the forces are in the same direction:

1. **Resultant Force Calculation**:
- The resultant force \( R \) when both forces are in the same direction is given by:
\[ R = P + Q \]
- Substituting the values:
\[ R = (25 \pm 0.2) + (16 \pm 0.7) \]
- This simplifies to:
\[ R = 25 + 16 \pm (0.2 + 0.7) \]
- Therefore:
\[ R = 41 \pm 0.9 \, \text{N} \]

### (ii) When the forces are in opposite directions:

1. **Resultant Force Calculation**:
- The resultant force \( R \) when the forces are in opposite directions is given by:
\[ R = P - Q \]
- Substituting the values:
\[ R = (25 \pm 0.2) - (16 \pm 0.7) \]
- This simplifies to:
\[ R = 25 - 16 \pm (0.2 + 0.7) \]
- Therefore:
\[ R = 9 \pm 0.9 \, \text{N} \]

### Final Results:
- When the forces are in the same direction: \( R = 41 \pm 0.9 \, \text{N} \)
- When the forces are in opposite directions: \( R = 9 \pm 0.9 \, \text{N} \)