Physics-
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Question

A particle of mass m is rotating in a horizontal circle of radius R and is attached to a hanging mass M as shown in the figure. The speed of rotation required by the mass m keep M steady is

  1. square root of fraction numerator m g R over denominator M end fraction end root    
  2. square root of fraction numerator m g R over denominator m end fraction end root    
  3. square root of fraction numerator m g over denominator M R end fraction end root    
  4. square root of fraction numerator m R over denominator M g end fraction end root    

The correct answer is: square root of fraction numerator m g R over denominator m end fraction end root


    To keep the mass M steady, let T is the tension in the string joining the two. Then for particle m comma
    T equals fraction numerator m v to the power of 2 end exponent over denominator R end fraction open parentheses i close parentheses
    For mass M comma
    T equals M g left parenthesis i i right parenthesis
    From Eqs. (i) and (ii)
    fraction numerator m v to the power of 2 end exponent over denominator R end fraction equals M g ⟹ v equals square root of fraction numerator M g R over denominator m end fraction end root

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