Question

Moment of inertia of a disc about the axis passing through the center and perpendicular to the plane is \(I_1\). What is the moment of inertia about its diameter?

• A. \(I_1/2\)
• B. \(I_1\)
• C. \(I_1/4\)
• D. \(2I_1\)

Hint:

For a disc, the moment of inertia about an axis through the center and perpendicular to the plane is half the product of mass and radius squared. For the diameter, it is reduced by a factor of 2.

Answer 1

The Correct Option is A

The moment of inertia \(I\) of a disc about an axis passing through the center and perpendicular to the plane is given by: \[ I_1 = \frac{1}{2} M R^2 \] Where \(M\) is the mass of the disc, and \(R\) is its radius. Now, the moment of inertia about the diameter can be found using the parallel axis theorem, which states: \[ I_{\text{diameter}} = I_{\text{center}} - \text{(mass)} \times \text{(distance from center to diameter)}^2 \] In this case, the distance from the center to the diameter is zero, and we obtain the formula for the moment of inertia about the diameter: \[ I_{\text{diameter}} = \frac{1}{4} M R^2 \] Thus, the moment of inertia about the diameter is \(I_1/2\).