A bucket containing water is revolved in a vertical circle of radius $$r$$. To prevent the water from falling down, the minimum frequency of revolution required is

($$\mathrm{g}=$$ acceleration due to gravity)

A body moving in a circular path with a constant speed has constant

Two bodies of masses '$$\mathrm{m}$$' and '$$3 \mathrm{~m}$$' are rotating in horizontal speed of the body of mass '$$m$$' is $$n$$ times that of the value of heavier body; while the centripetal force is same for both. The value of $$n$$ is

The angle of banking '$$\theta$$' for a meter gauge railway line is given by $$\theta=\tan ^{-1}\left(\frac{1}{20}\right)$$. What is the elevation of the outer rail above the inner rail?