Q: What is the displacement of the point of a wheel initially in contact with the ground when the wheel rolls forward half a revolution ? Take the radius of the wheel as R and the X -axis as the forward direction ?

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Sol: Distance covered by the point in horizontal & vertical direction is X = πR , Y = 2R respectively

Displacement of point of wheel $ = \sqrt{X^2 + Y^2}$

$ = \sqrt{(\pi R)^2 + (2R)^2}$

$ = R\sqrt{\pi^2 + 4}$