The five solids shown in the figure below have equal heights, widths, and masses

Question

The five solids shown in the figure below have equal heights, widths, and masses. The axes of rotation are located at the center of each object and are perpendicular to the plane of the paper. Rank the moments of inertia from greatest to least. Hoop Cube Solid cylinder Solid sphere Hollow sphere Hoop > Cube > Hollow sphere > Solid cylinder-Solid sphere Hoop > Cube > Solid cylinder > Hollow sphere > Solid sphere Cube > Hoop > Hollow sphere = Solid cylinder > solid sphere Hoop Cube > Hollow sphere > Solid sphere > Solid cylinder Hoop > Cube Hollow sphere >Solid cylinder > Solid sphere

Explanation / Answer

Moment of Inertia of

1) Hoop = MR^2 = 1

2) Solid Cube = 1/6 * MR^2 = 0.1667

3) Solid Cylinder = 1/2 * MR^2 = 0.5

4) Solid Sphere = 2/5 * MR^2 = 0.4

5) Hallow Sphere = 2/3 * MR^2 = 0.6667

Hence, None of the options is Correct

Atleast the last one equal to symbol replaced with greater than symbol would be correct.

Hoop>Cube=Hollow sphere>Solid Cylinder > Solid Sphere

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