A body is rotating uniformly about a vertical axis fixed in an inertial frame. The resultant force on a particle of the body not on axis is

Options

A. vertical
B. horizontal skew with the axis
C. horizontal and intersecting the axis
D. none of these

Answer

To solve the problem, we need to analyze the forces acting on a particle of a body that is rotating uniformly about a vertical axis. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Setup
We have a body rotating about a vertical axis with a uniform angular velocity (ω). A particle P on the body is located at a distance r from the axis of rotation.

**Hint:** Visualize the rotation and the position of the particle relative to the axis.

### Step 2: Identify the Forces Acting on the Particle
When the body rotates, the particle experiences a centripetal force directed towards the axis of rotation. This force is necessary to keep the particle moving in a circular path.

**Hint:** Remember that centripetal force is always directed towards the center of the circular path.

### Step 3: Determine the Direction of the Resultant Force
Since the particle is moving in a circle, the only force acting on it (in the horizontal plane) is the centripetal force, which acts radially inward towards the axis of rotation. There are no other vertical forces acting on the particle since it is in a uniform rotation.

**Hint:** Consider the nature of uniform circular motion and the forces involved.

### Step 4: Analyze the Resultant Force
The resultant force on the particle is thus horizontal and directed towards the axis of rotation. This means that the resultant force is not only horizontal but also intersects the vertical axis of rotation at some point.

**Hint:** Visualize how the resultant force would appear in a diagram.

### Step 5: Conclusion
The resultant force on a particle of the body not on the axis is horizontal and intersects the axis of rotation.

### Final Answer
The correct option is that the resultant force on a particle of the body not on the axis is horizontal and intersects the axis.

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