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Question

# A point P (on a wheel) is the contact point of the wheel and the ground. The wheel rolls on the ground without slipping. The value of displacement of the point P, when the wheel completes half a rotation is (if radius of wheel is 1 m)

A
2 m
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B
π2+4 m
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C
π m
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D
π2+2 m
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Solution

## The correct option is B √π2+4 m Given, the wheel rolls without slipping. Hence, the distance covered by the point P in horizontal direction will be equal to the half of the perimeter of the circle i.e 2πR2=πR In half rotation, point P will be at the top as shown in figure. Thus, displacement of point P (by Pythagoras theorem) r=√(πR)2+(2R)2 r=R√π2+4 (∵R=1 m) r=√π2+4 m

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