Q27 / 223 · NTA Abhyas (NEET) 2020 · Physics · Rotational Motion

For the same total mass of the following will have the largest moment of inertia an axis passing through the centre of mass and perpendicular to the plane of the body

  • A
    A disc of radius a
  • B
    A ring of radius a
  • C
    A square lamina of side 2a
  • Correct answer
    D
    Four rods forming a square of side 2a

Solution

MI of disk of radius a about given axis is m a 2 /2

MI of ring of radius a about given axis is m a 2

MI of square of side 2a about given axis is m ( 2a ) 2 /6 =2m a 2 /3

MI of four rods forming square of side 2a about given axis is 4× m ( 2a ) 2 / 12 +m a 2 =4m a 2 /3

So among all options four rods forming square of side 2a has highest moment of inertia of 4m a 2 /3 about an axis passing through its center of mass and perpendicular to the plane of body.

Hence, the correct answer is option: 'D'.

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