A bead of mass $\frac {1}{2}\,kg$ starts from rest from $A$ to move in a vertical plane along a smooth fixed quarter ring of radius $5\,m$, under the action of a constant horizontal force $F = 5\,N$ as shown. The speed of bead as it reaches the point $B$ is ……………. $\mathrm{m}/ \mathrm{s}$ [Take $g = 10\,m/s^2$ ]

A frictionless track $ABCDE$ ends in a circular loop of radius $R$. A body slides down the track from point $A$ which is at a height $h = 5\, cm$. Maximum value of $R$ for the body to successfully complete the loop is ……….. $\mathrm{cm}$

A bob of mass m suspended by a light string of length $L$ is whirled into a vertical circle as shown in figure. What will be the trajectory of the particle, if the string is cut at $(a)$ point $B$ ? $(b)$ point $C$ ? $(c) $ point $X$ ?

A stone of mass $m$, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

A bucket full of water is revolved in vertical circle of radius $2\,m$. What should be the maximum time-period of revolution so that the water doesn't fall off the bucket ……… $\sec$.