A uniform circular disc of radius ' $\mathrm{R}^{\prime}$ and mass ' $\mathrm{M}^{\prime}$ is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius $R / 2$ is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.

A thin circular disc of mass $$\mathrm{M}$$ and radius $$\mathrm{R}$$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $$\omega$$. If another disc of same dimensions but of mass $$\mathrm{M} / 2$$ is placed gently on the first disc co-axially, then the new angular velocity of the system is :

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis $$A B$$ as shown in figure is $$\sqrt{8 / x}$$. The value of $$x$$ is :