Four particles each of mass $$1 \mathrm{~kg}$$ are placed at four corners of a square of side $$2 \mathrm{~m}$$. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is _____ $$\mathrm{kgm}^2$$.

A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be _________ rad s$$^{-2}$$.

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $$\pi: 22$$ then, the value of its angular speed will be ____________ $$\mathrm{rad} / \mathrm{s}$$.