A particle is whirled in a vertical circle of radius $1.0\  m$ using a string with one end fixed. If the ratio of maximum and minimum tension in the string is $\frac{5}{3}$, the minimum velocity of the particle during circular motion is    ……… $ms^{-1}$

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 bob of mass $10$ $M$ is suspended through an inextensible string of length $l$. When the bob is at rest at the equilibrium position, two particles of mass $m$ each moving with velocity $u$ making an angle $60^o $ with the string strike and get simultaneously attached to the bob. What is the value of impulsive tension $(l)$ in the string during the impact ?

A particle of mass $m$ , attached with a string of length $l$ is moving in a vertical circle. If the particle is just looping the loop without slackening of the string and $v_A, v_B, v_D$ are speeds at positions $A, B, D$ shown in figure, then

A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles $30^o $ and $60^o $ from vertical (lowest position) are $T_1 and T_2$ respectively. then