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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.
  1. 2 m
  2. π2+4 m
  3. π m
  4. π2+2 m


Solution

The correct option is B π2+4 m
When 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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