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Concepts Of Physics MCQ Edition [Volume 1]PhysicsRotational Mechanics

Let I_A and I_B denote the moments of inertia of a body about two axes A and B , respectively. Axis A passes through the body's centre of mass, whereas axis B does not.

Options

  1. AIf I_A < I_B , the axes are parallel
  2. BI_A < I_B
  3. CIf the axes are parallel, I_A < I_B
  4. DIf the axes are not parallel, I_A I_B

Correct answer

C. If the axes are parallel, I_A < I_B

Step-by-step solution

According to the parallel axis theorem, the moment of inertia of a body about any axis is equal to the sum of its moment of inertia about a parallel axis passing through its centre of mass and the product of its mass and the square of the perpendicular distance between the two axes. Let axis A pass through the centre of mass and axis B be parallel to axis A at a perpendicular distance d . Then, I_B = I_A + Md^2 Since axis B does not pass through the centre of mass, d 0 , which implies Md^2 > 0 . Therefore, I_B > I_

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