Eleven forces each equal to 5N act on a particle simultaneously. If each force makes an angle 30° with the next one, the resultant of all forces is

Options

A. 15N
B. 55 N
C. 5 N
D. zero

Answer

To find the resultant of the eleven forces each equal to 5 N acting at an angle of 30° with respect to each other, we can follow these steps:

### Step 1: Understand the Configuration of Forces
We have 11 forces, each with a magnitude of 5 N. Each force is separated by an angle of 30° from the next force.

### Step 2: Calculate the Total Angle
Since there are 11 forces, the total angle they would cover is:
\[ \text{Total angle} = (11 - 1) \times 30° = 300° \]
This means that the forces are not completing a full circle (360°), which is important for understanding how they combine.

### Step 3: Determine the Minimum Forces for Zero Resultant
To achieve a zero resultant, we need to consider how many forces would be required to cancel each other out. The minimum number of forces required to achieve a zero resultant is determined by:
\[ \text{Minimum forces for zero resultant} = \frac{360°}{30°} = 12 \]
Since we only have 11 forces, we cannot achieve a zero resultant.

### Step 4: Analyze the Remaining Force
Since we have 11 forces and need 12 for a zero resultant, we conclude that 10 of these forces will effectively cancel each other out, leaving us with one unopposed force.

### Step 5: Calculate the Resultant Force
The only remaining force that does not get canceled out is one of the 5 N forces. Therefore, the resultant of all the forces acting on the particle is:
\[ \text{Resultant} = 5 \, \text{N} \]

### Conclusion
Thus, the resultant of all 11 forces acting on the particle is 5 N.