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)

Four spheres each of diameter $$2 a$$ and mass $$m$$ are placed in a way that their centers lie on the four corners of a square of side $$b$$. Moment of inertia of the system about an axis along one of the sides of the square is