A solid sphere of mass , radius, and having a moment of inertia about an axis passing through the center of mass as is recast into a disc of thickness , whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains . Then, the radius of the disc will be
Step 1: Given data
The mass of the sphere is .
The radius of the sphere is .
The moment of inertia of the sphere is
The moment of inertia of the disc is .
Step 2: Moment of inertia
Step 3: Moment of inertia of a solid sphere and a disc.
Step 4: Diagram
Step 5: Finding the radius of the disc
According to the question, in both cases, the moment of inertia is the same, i.e, .
Therefore, the radius of the disc is .