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A small bead of mass m = 1 kg is free to move on a circular hoop. The circular hoop has centre at C and radius r = 1 m and it rotates about a fixed vertical axis. The coefficient of friction between bead and hoop is µ = 0.5. The maximum angular speed of the hoop for which the bead does not have relative motion with respect to hoop, at the position shown in figure is : (Take g = 10 m/s2)

  1. left parenthesis 5 square root of 2 right parenthesis to the power of 1 divided by 2 end exponent    
  2. left parenthesis 10 square root of 2 right parenthesis to the power of 1 divided by 2 end exponent    
  3. left parenthesis 15 square root of 2 right parenthesis to the power of 1 divided by 2 end exponent    
  4. left parenthesis 30 square root of 2 right parenthesis to the power of 1 divided by 2 end exponent    

The correct answer is: left parenthesis 30 square root of 2 right parenthesis to the power of 1 divided by 2 end exponent


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