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Question: Given that P is a point on a wheel rolling on a horizontal ground. The radius of the wheel is R. Ini...

Given that P is a point on a wheel rolling on a horizontal ground. The radius of the wheel is R. Initially if the point P is in contact with the ground the wheel rolls through half the revolution. What is the displacement of point P?

A

Rπ2+1\sqrt{\pi^{2} + 1}

B

Rπ2+4\sqrt{\pi^{2} + 4}

C

πR

D

2πR

Answer

Rπ2+4\sqrt{\pi^{2} + 4}

Explanation

Solution

Displacement of = πRi^\widehat{i} + 2Rj^\widehat{j}

Displacement of P = (πR)2+(2R)2=Rπ2+4\sqrt{(\pi R)^{2} + (2R)^{2}} = R\sqrt{\pi^{2} + 4}