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Question

A wheel of radius 1 m rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is

A
2π
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B
2π
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C
π2+4
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D
π
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Solution

The correct option is C π2+4
Consider point A as the point of contact of the wheel with ground.

We know for one full revolution, the wheel traces 2πR distance. So for half the revolution it will trace πR distance.

So, the displacement:
AA=(2R)2+(πR)2AA=4+π2

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