Two non-collinear forces, one of 10 N and another of 6 N act upon a body. The directions of the forces are unknown. The resultant force on the body is :

Options

A. between 6 and 10 N
B. between 4 and 16 N
C. more than 6 N
D. more than 10 N

Explanation

To find the resultant force acting on a body due to two non-collinear forces of 10 N and 6 N, we can follow these steps:

### Step 1: Identify the Forces
We have two forces:
- \( F_1 = 10 \, \text{N} \)
- \( F_2 = 6 \, \text{N} \)

### Step 2: Determine the Minimum Resultant Force
The minimum resultant force occurs when the two forces are acting in opposite directions. The formula for the minimum resultant \( R_{\text{min}} \) is:
\[ R_{\text{min}} = |F_1 - F_2| \]
Calculating this:
\[ R_{\text{min}} = |10 \, \text{N} - 6 \, \text{N}| = |4 \, \text{N}| = 4 \, \text{N} \]

### Step 3: Determine the Maximum Resultant Force
The maximum resultant force occurs when the two forces are acting in the same direction. The formula for the maximum resultant \( R_{\text{max}} \) is:
\[ R_{\text{max}} = F_1 + F_2 \]
Calculating this:
\[ R_{\text{max}} = 10 \, \text{N} + 6 \, \text{N} = 16 \, \text{N} \]

### Step 4: Determine the Range of the Resultant Force
Since the forces are non-collinear, the resultant force will lie between the minimum and maximum resultant forces:
\[ R_{\text{min}} < R < R_{\text{max}} \]
This gives us:
\[ 4 \, \text{N} < R < 16 \, \text{N} \]

### Conclusion
The resultant force acting on the body is between 4 N and 16 N.

### Final Answer
The resultant force on the body is between 4 N and 16 N.

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