Physics
Mechanics
Easy

Question

Seven identical disc are arranged in a hexagonal, planar pattern so as to touch each neighbour, as shown in the figure. Each disc has mass m and radius r. What is the moment of inertia of the system of seven disks about an axis passing through the centre of central disk and normal to plane of all disks?

  1. 7 over 2 m r squared
  2. 13 over 2 m r squared
  3. 29 over 2 m r squared
  4. 55 over 2 m r squared

The correct answer is: 55 over 2 m r squared


    I equals I subscript 0 plus 6 I to the power of straight prime
    I subscript 0 is the moment of inertia of central disc and I' is moment of inertia of rest of the each disc about  specified axis.
    By parallel axes theorem
    I equals fraction numerator m r squared over denominator 2 end fraction plus 6 left parenthesis I subscript cm plus m d squared right parenthesis equals fraction numerator m r squared over denominator 2 end fraction plus 6 left square bracket fraction numerator m r squared over denominator 2 end fraction plus m left parenthesis 2 r right parenthesis squared right square bracket
    equals fraction numerator m r squared over denominator 2 end fraction plus fraction numerator 6 m r squared over denominator 2 end fraction plus 24 m r squared equals fraction numerator 55 m r squared over denominator 2 end fraction

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