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Question

# A point P is the contact point of wheel on the ground which rolls on ground without slipping. Find the value of displacement of the point P when wheel completes half revolution. Radius of the 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 mWhen a body is under pure rolling then the moment it completes 1 revolution, the horizontal distance covered is equal to perimeter of circle i.e 2πr given, radius of wheel is r=1 m Initial position, P is in contact with ground After 12 revolution it reached the highest point B on wheel. ⇒ Horizontal distance PA given by, x=2πr2=πr=π×1 From the right angled triangle ΔPBA, applying pythagoras theorem: PB=√PA2+AB2=√(π×1)2+(2×1)2 ∴Displacement of point P , PB=√π2+4 m

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