A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in the figure. Consider an axis $X{X}^{\mathit{\prime }}$ which is touching the two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about $X{X}^{\mathit{\prime }}$ axis is:

Point masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ are placed at the opposite ends of rigid rod of length $\text{L}$, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $\text{L}$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity ${\mathrm{\omega }}_0$ is minimum, is given by: