Question

A point \(P\) on the wheel of radius \(R\) is initially in contact with the ground. When the wheel rolls forward half a revolution, the displacement of the point \(P\) is:

• A. \( R \)
• B. \( \pi R \)
• C. \( R \sqrt{\pi^2 + 4} \)
• D. \( R \sqrt{\pi + 4} \)

Hint:

The displacement of a point on a rolling wheel combines both translational and rotational motion. For half a revolution, this results in the formula \( R \sqrt{\pi^2 + 4} \).

Answer 1

The Correct Option is C

The displacement of the point \(P\) is derived by considering the combined effect of the wheel's forward motion and rotation. The total displacement when the wheel rolls half a revolution is \( R \sqrt{\pi^2 + 4} \), as derived from the geometric relation between the point's path and the wheel's radius.