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Question

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

  1. 2 pi  
  2. square root of 2 pi  
  3. square root of pi to the power of 2 end exponent plus 4 end root  
  4. pi  

The correct answer is: square root of pi to the power of 2 end exponent plus 4 end root


    Horizontal distance covered by the wheel in half revolution equals pi R

    So the displacement of the point which was initially in contact with ground
    equals A A to the power of ´ end exponent equals square root of open parentheses pi R close parentheses to the power of 2 end exponent plus open parentheses 2 R close parentheses to the power of 2 end exponent end root
    equals R square root of pi to the power of 2 end exponent plus 4 end root equals square root of pi to the power of 2 end exponent plus 4 end root blank left square bracketAsblank R equals 1 m right square bracket

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