Consider a disc of radius $$R$$ and mass $$M$$. A hole of radius $$\frac{R}{3}$$ is created in the disc, such that the centre of the hole is $$\frac{R}{3}$$ away from centre of the disc. The moment of inertia of the system along the axis perpendicular to the disc passing through the centre of the disc is

As solid sphere of mass $$M$$ and radius $$R$$ spins about an axis passing through its centre making $$600 \mathrm{~rpm}$$. Its kinetic energy of rotation is

Two fly wheels $$A$$ and $$B$$ are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are $$5.0 \mathrm{~kg}-\mathrm{m}^2$$ and $$20.0 \mathrm{~kg}-\mathrm{m}^2$$, respectively. Wheel $$A$$ is made to rotate at $$10 \mathrm{~rev}$$ per second. Wheel $$B$$, initially stationary, is now coupled to $$A$$ with the help of a clutch. The rotation speed of the wheels will become

A sphere and a hollow cylinder without slipping, roll down two separate inclined planes A and B, respectively. They cover same distance in a given duration. If the angle of inclination of plane A is 30$$^\circ$$, then the angle of inclination of plane B must be (approximately)