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What is the displacement of the point on the wheel initially in contact with the ground when the wheel rolls forwards half of revolution ? Take the radius of the wheel as ‘R’ and the x-axis in the forward direction

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$R \sqrt{π^{2} + 9}, {Tan}^{- 1} (\frac{3}{π}) with x -axis$

$R \sqrt{π^{2} + 16}, {Tan}^{- 1} (\frac{4}{π}) with x -axis$

None

$R \sqrt{π^{2} + 4} and angle {Tan}^{- 1} (\frac{2}{π}) with x -axis$

answer is B.

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Detailed Solution

Displacement $= \vec{{PP}^{1}} \Rightarrow |\vec{{PP}^{1}}| = \sqrt{{PM}^{2} + {MP}^{1^{2}}}$

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

$Tan θ = (\frac{2 R}{π R}) \Rightarrow θ = {Tan}^{- 1} (\frac{2}{π})$

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