$A$ bucket tied at the end of a $1.6\, m$ long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill,when the bucket is at the highest position? (Take $g = 10\, m/s^2$)

$A$ body of mass $m$ is suspended from a string of length $l$. What is the minimum horizontal velocity that should be given to the body in its lowest position so that it may complete one full revolution in a vertical plane with the point of suspension as the center of the circle?

$A$ body of mass $m$ hangs at one end of a string of length $l$,the other end of which is fixed. It is given a horizontal velocity such that the string just reaches a position where it makes an angle of $60^{\circ}$ with the vertical. The tension in the string at the mean position is:

$A$ wire,which passes through the hole of a small bead,is bent in the form of a quarter of a circle. The wire is fixed vertically on the ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$,the force it applies on the wire is

$A$ body of mass $m$ is tied to a string of length $l$ and rotated in a vertical circle. What is the difference in tension between the lowest point and the highest point (in $,mg$)?

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 .........