Answer:
To solve this problem, let's think about the path traced by the point initially in contact with the ground as the wheel rolls forward.
Given:
The radius of the wheel is 1m.
The wheel rolls forward half a revolution.
Step 1: Understand the motion of the point.
As the wheel rolls forward, the point initially in contact with the ground will trace a cycloid curve. A cycloid is the curve traced by a point on the circumference of a circle as it rolls along a straight line.
Step 2: Calculate the distance traveled by the center of the wheel.
For half a revolution, the center of the wheel will move forward by a distance equal to the radius of the wheel (1m) multiplied by π (half the circumference).
Distance traveled by the center = 1m × π = π meters
Step 3: Determine the magnitude of the displacement of the point.
The magnitude of the displacement of the point will be equal to the length of the chord connecting the initial and final positions of the point on the cycloid curve. This chord is parallel to the ground and has a length equal to the diameter of the wheel (2m).
Magnitude of the displacement = 2m
Therefore, the correct answer is a) 2π.
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