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The minimum speed for a particle at the lowest point of a vertical circle of radius r, to describe the circle is v. If the radius of the circle is reduced to one-fourth its value, the corresponding minimum speed will be

  1. v over 4    
  2. v over 2    
  3. 2v    
  4. 4v    

The correct answer is: v over 2


    v equals square root of 5 g R end root
    When R to the power of ´ end exponent equals fraction numerator R over denominator 4 end fraction
    v to the power of ´ end exponent equals square root of 5 g R ´ end root equals square root of 5 g R divided by 4 end root equals fraction numerator 1 over denominator 2 end fraction square root of 5 g R end root equals fraction numerator 1 over denominator 2 end fraction v

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