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Four balls each of radius 10 cm and mass 1 kg, 2kg, 3 kg and 4 kg are attached to the periphery of massless plate of radius 1 m. What is moment of inertia of the system about the centre of plate?

  1. 12.04 kg-m to the power of 2 end exponent    
  2. 10.04 kg-m to the power of 2 end exponent    
  3. 11.50 kg-m to the power of 2 end exponent    
  4. 5.04 kg-m to the power of 2 end exponent    

The correct answer is: 10.04 kg-m to the power of 2 end exponent


    Moment of inertia of the system about the centre of plane is given by
    I equals open square brackets fraction numerator 2 over denominator 5 end fraction cross times 1 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 1 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
    plus open square brackets fraction numerator 2 over denominator 5 end fraction cross times 2 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 2 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
    plus open square brackets fraction numerator 2 over denominator 5 end fraction cross times 3 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 3 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
    plus open square brackets fraction numerator 2 over denominator 5 end fraction cross times 4 cross times open parentheses 0.1 close parentheses to the power of 2 end exponent plus 4 cross times open parentheses 1 close parentheses to the power of 2 end exponent close square brackets
    equals 1.004 plus 2.008 plus 3.012 plus 4.016
    equals 10.04 blank k g minus m to the power of 2 end exponent

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