question_answer 46)

                  Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?                

Answer:

                  We know that moment of inertia, \[I=\sum{m{{r}^{2}}}\]. In case of a hollow cylinder of radius R, all its mass  \[(m)\] lies at a distance R from the axis of symmetry. But in case of solid sphere of radius R and mass M, most of its mass lies at a distance smaller than R. Hence, \[{{I}_{\text{cylinder}}}>{{I}_{\text{solid}}}\] (about the axes of symmetry).