Two forces of `12N` and `8N` act upon a body. The resultant force on the body maximum value of

Options

A. `4N`
B. `0N`
C. `20N`
D. `8N`

Answer

To find the maximum resultant force when two forces of 12 N and 8 N act on a body, we can use the formula for the resultant of two vectors. The maximum resultant occurs when the two forces are acting in the same direction.

### Step-by-Step Solution:

1. **Identify the Forces**:
We have two forces:
- \( F_1 = 12 \, \text{N} \)
- \( F_2 = 8 \, \text{N} \)

2. **Use the Formula for Resultant Force**:
The resultant force \( R \) when two forces are acting at an angle \( \theta \) is given by:
\[ R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2\cos(\theta)} \]
For maximum resultant, we consider \( \theta = 0^\circ \) (forces are in the same direction), where \( \cos(0) = 1 \).

3. **Substituting Values**:
Substitute \( F_1 \) and \( F_2 \) into the formula:
\[ R = \sqrt{12^2 + 8^2 + 2 \cdot 12 \cdot 8 \cdot \cos(0)} \]
\[ R = \sqrt{12^2 + 8^2 + 2 \cdot 12 \cdot 8 \cdot 1} \]

4. **Calculate Each Term**:
Calculate \( 12^2 \) and \( 8^2 \):
\[ 12^2 = 144 \]
\[ 8^2 = 64 \]
Now calculate \( 2 \cdot 12 \cdot 8 \):
\[ 2 \cdot 12 \cdot 8 = 192 \]

5. **Combine the Values**:
Now combine these values:
\[ R = \sqrt{144 + 64 + 192} \]
\[ R = \sqrt{400} \]

6. **Final Calculation**:
Finally, calculate the square root:
\[ R = 20 \, \text{N} \]

### Conclusion:
The maximum resultant force on the body is **20 N**.