Seven identical discs are arranged in a planar pattern, so as to touch each other as shown in the figure. Each disc has mass $$m$$ radius $$R$$. What is the moment of inertia of system of six discs about an axis passing through the centre of central disc and normal to plane of all discs?

The angular speed of a motor wheel is increased from $$1200 \mathrm{~rpm}$$ to $$3120 \mathrm{~rpm}$$ in $$16 \mathrm{~s}$$. The angular acceleration of the motor wheel is

In figure $$E$$ and $$v_{\mathrm{cm}}$$ represent the total energy and speed of centre of mass of an object of mass $$1 \mathrm{~kg}$$ in pure rolling. The object is