A point marked on a ring of radius 2 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:

Step-by-step solution

Let the radius of the ring be R = 2 cm. Initially, the point is at the origin (0, 0) in contact with the horizontal plane (X-axis). The ring rolls forward by half a revolution. The distance moved by the center of the ring is d = R _ rot = R = 2 . After half a revolution, the center of the ring is at (2 , 2) . The point, which was initially at the bottom, is now at the top of the ring. The coordinates of the point after half a revolution are (2 , 2R) = (2 , 4) . The displacement vector S of the point from its initia