Out of the following set of forces, the rsultant of which cannot be zero?

Options

A. 10,10,10
B. 10,10,20
C. 10,20,20
D. 10,20,40

Explanation

To determine which set of forces cannot have a resultant of zero, we can use the triangle law of vector addition. According to this law, for three forces to be in equilibrium (resultant equal to zero), the sum of the magnitudes of any two forces must be greater than or equal to the magnitude of the third force.

Let's analyze the given options step by step:

### Step 1: Identify the given sets of forces
Assume we have the following sets of forces:
1. Set A: 10 N, 20 N, 30 N
2. Set B: 10 N, 20 N, 40 N
3. Set C: 15 N, 25 N, 35 N
4. Set D: 5 N, 5 N, 5 N

### Step 2: Apply the triangle law of vector addition
We will check each set of forces to see if the condition for the resultant being zero is satisfied.

#### Set A: 10 N, 20 N, 30 N
- Check: 10 + 20 = 30 (equal to the third force)
- Resultant can be zero.

#### Set B: 10 N, 20 N, 40 N
- Check: 10 + 20 = 30 (less than the third force, 40)
- Resultant cannot be zero.

#### Set C: 15 N, 25 N, 35 N
- Check: 15 + 25 = 40 (greater than the third force, 35)
- Resultant can be zero.

#### Set D: 5 N, 5 N, 5 N
- Check: 5 + 5 = 10 (greater than the third force, 5)
- Resultant can be zero.

### Step 3: Conclusion
From the analysis, we find that the set of forces 10 N, 20 N, and 40 N cannot have a resultant of zero because the sum of the two smaller forces is less than the largest force.

### Final Answer
The resultant of the forces 10 N, 20 N, and 40 N cannot be zero.

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