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?

A particle moves in a circular orbit of radius '$$r$$' under a central attractive force, $$F=-\frac{k}{r}$$, where $$\mathrm{k}$$ is a constant. The periodic time of its motion is proportional to

A particle at rest starts moving with a constant angular acceleration of $$4 \mathrm{~rad} / \mathrm{s}^2$$ in a circular path. At what time the magnitude of its centripetal acceleration and tangential acceleration will be equal?

In non-uniform circular motion, the ratio of tangential to radial acceleration is ($$r=$$ radius, $$\alpha=$$ angular acceleration and $$v=$$ linear velocity)