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General
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Question

A wire of 9.8 cross times 1 0 to the power of negative 3 end exponent k g m to the power of negative 1 end exponent passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of 30° with the horizontal. Masses m and M are tied at the two ends of wire such that m rests on the plane and M hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of 100 ms–1. Chose the correct option

  1. m equals 20 k g    
  2. m equals 5 k g    
  3. m equals 2 k g    
  4. m equals 7 k g    

The correct answer is: m equals 20 k g


    v equals square root of fraction numerator T over denominator mu end fraction end root

    For equilibrium M g equals m g sin invisible function application 3 0 equals T
    Þ M equals fraction numerator m over denominator 2 end fraction Þ 100 equals square root of fraction numerator M g over denominator 9.8 cross times 1 0 to the power of negative 3 end exponent end fraction end root equals square root of fraction numerator M left parenthesis 9.8 right parenthesis over denominator 9.8 cross times 1 0 to the power of negative 3 end exponent end fraction end root
    Þ 100 equals square root of M left parenthesis 1000 right parenthesis end root Þ M equals 10 k g and m equals 20 k g

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