$A$ bucket full of water is revolved in a vertical circle of radius $2\,m$. What should be the maximum time-period of revolution so that the water does not fall off the bucket? (Take $g = 10\,m/s^2$) ......... $\sec$.

$A$ small sphere of mass $m$ is suspended by a light and inextensible string of length $l$ from a point $O$ fixed on a smooth inclined plane of inclination $\theta$ with the horizontal. The sphere is moving in a circle on the incline as shown. If the sphere has a velocity $u$ at the top most position $A$, then:

In the figure shown,a particle is released from the position $A$ on a smooth track. When the particle reaches at $B$,then the normal reaction on it by the track is .........

$A$ body of mass $m \ kg$ slides from rest along the curve of a vertical circle from point $A$ to $B$ on a frictionless path. The velocity of the body at $B$ is: (Given: $R = 14 \ m$,$g = 10 \ m/s^2$,and $\sqrt{2} = 1.4$) (in $m/s$)

$A$ mass $m$ is released from point $A$ as shown in the figure. The tension in the string at point $B$ will be:

$A$ particle starts sliding from the top of a sphere of diameter $42 \, m$. At what height from the bottom of the sphere will the particle lose contact with the sphere?