A hollow sphere has radius $6.4 \,m$. Minimum velocity required by a motor cyclist at bottom to complete the circle will be ……….. $m/s$

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 body of mass $0.4\, kg$ is whirled in a vertical circle making $2\, rev/sec$. If the radius of the circle is $2\, m$, then tension in the string when the body is at the top of the circle, is ……… $N$

A stone of mass $1\, kg$ tied to a light inextensible string of length $L = \frac{{10}}{3}m$ is whirling in a circular path of radius $L$ in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is $4$ and if $g$ is taken to be $10m/{\sec ^2}$, the speed of the stone at the highest point of the circle is ……. $m/\sec$

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 ?