100 coplanar forces each equal to 10 N act on a body. Each force makes angle `(pi)/(50)` with the preceding force. What is the resultant of the forces

Options

A. 1000N
B. 500N
C. 250N
D. zero

Explanation

To solve the problem of finding the resultant of 100 coplanar forces, each equal to 10 N and making an angle of \(\frac{\pi}{50}\) radians with the preceding force, we can follow these steps:

### Step 1: Understand the Configuration of Forces
We have 100 forces acting on a body, each with a magnitude of 10 N. Each force is separated by an angle of \(\frac{\pi}{50}\) radians from the preceding force. This means that the forces are arranged in a circular manner around a point.

### Step 2: Calculate the Total Angle
The total angle formed by the 100 forces can be calculated as:
\[ \text{Total Angle} = \text{Number of Forces} \times \text{Angle between Forces} = 100 \times \frac{\pi}{50} = 2\pi \]
This indicates that the forces complete a full circle.

### Step 3: Analyze the Resultant of the Forces
When forces are arranged in such a way that they complete a full circle (i.e., the total angle is \(2\pi\)), they form a closed polygon. In this case, since the forces are evenly distributed around a point, they will cancel each other out.

### Step 4: Conclusion
Since the forces form a closed polygon, the resultant of all these forces is zero. Therefore, the resultant force acting on the body is:
\[ \text{Resultant} = 0 \, \text{N} \]

### Final Answer
The resultant of the forces is \(0 \, \text{N}\).

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