Question

A flat disk, a solid sphere, and a hollow sphere each have the same mass m and radius r. The three objects are arranged so that an axis of rotation passes through the center of each object. The rotation axis is perpendicular to the plane of the flat disk. Which of the three objects has the largest moment of inertia?

Answer 1

Answer:

$I_{disc} = \frac{1}{2}mR^2$

$I_{sphere} = \frac{2}{5}mR^2$

$I_{hollow} = \frac{2}{3}mR^2$

so largest moment of inertia is for Hollow Sphere

Explanation:

Moment of inertia flat disc is given as

$I_{disc} = \frac{1}{2}mR^2$

moment of inertia of solid sphere

$I_{sphere} = \frac{2}{5}mR^2$

moment of inertia of hollow sphere

$I_{hollow} = \frac{2}{3}mR^2$

all the three objects are given with same mass and same radius

so largest moment of inertia is for Hollow Sphere