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Pure Rolling

Given #160;...

Question

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 revolution. What is the displacement of point $P$ ?

A

R \sqrt{π^{2} + 1}

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B

R \sqrt{π^{2} + 4}

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C

π R

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D

2 π R

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Solution

The correct option is A $R \sqrt{π^{2} + 4}$
Displacement of $P \Rightarrow π R \to i + 2 R \to j$
Displacement of $P \Rightarrow \sqrt{{(2 R)}^{2} + {(π R)}^{2}} = R \sqrt{4 + π^{2}}$

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