A body of mass $$5 \mathrm{~kg}$$ moving with a uniform speed $$3 \sqrt{2} \mathrm{~ms}^{-1}$$ in $$X-Y$$ plane along the line $$y=x+4$$. The angular momentum of the particle about the origin will be _________ $$\mathrm{kg} \mathrm{~m}^2 \mathrm{~s}^{-1}$$.

A cylinder is rolling down on an inclined plane of inclination $$60^{\circ}$$. It's acceleration during rolling down will be $$\frac{x}{\sqrt{3}} m / s^2$$, where $$x=$$ ________ (use $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is $$\frac{7}{x}$$, where $$x$$ is _________.

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 _____ $$\mathrm{kgm}^2$$.