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The moment of inertia of a body about an axis passing through the center of mass is Icm. If the mass of the body is m, find the moment of inertia about an axis parallel to the center of mass and at a distance of R from it.
1. I = Icm = MR2
2. I = Icm + MR2
3. I = Icm × MR2
4. I = Icm - MR2

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Correct Answer - Option 2 : I = Icm + MR2

CONCEPT:  

  • Moment of Inertia: A quantity expressing a body's tendency to resist angular acceleration, that is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation, is called the moment of Inertia.
  • Parallel Axis Theorem: The moment of inertia of a body about an axis parallel to the body passing through its center of mass is equal to the sum of the moment of inertia of the body about the axis passing through the center of mass and product of the mass of the body times the square of the distance between the two axes.


I = Icm + MR2

where I is the moment of inertia about an axis passing through the center of the to the plane of M is the mass of the body, R is the distance between axis and center of mass, Icm is the MOI about the center of mass.

EXPLANATION:

  • Given that Moment of inertia of a body about an axis passing through the center of mass is Icm.


Mass = m and I = moment of inertia at r distance from Icm

  • Parallel Axis Theorem: The moment of inertia of a body about an axis parallel to the body passing through its center of mass is equal to the sum of the moment of inertia of the body about the axis passing through the center of mass and product of the mass of the body times the square of the distance between the two axes.

I = Icm + MR2

  • So, the moment of inertia about an axis parallel to the center of mass and at a distance of R will be:

I = Icm + MR2

So the correct answer is option 2.

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