A point marked on a ring of radius \(2\,\text{cm}\) is in contact with a horizontal plane. Now the ring is rolled forward half a revolution along the positive X direction. Then the angle made by the displacement vector of the point with the X-axis is:
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For rolling without slipping, distance travelled by centre equals arc length \(R\theta\). For half revolution, horizontal displacement is \(\pi R\), while the marked bottom point rises by \(2R\).