$A$ rod of length $L$ is hung from one of its ends,and a mass $m$ is attached to its free end. What tangential velocity must be imparted to $m$ so that it reaches the top of the vertical circle? ($g$ = acceleration due to gravity)

In a circus,a stuntman rides a motorbike on a vertical circular track of radius $r$. Find the minimum speed he must maintain at the highest point of the track.

$A$ 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 $10\, m/s^2$,the speed of the stone at the highest point of the circle is ....... $m/s$.

The mass of the $bob$ of a simple pendulum of length $L$ is $m$. If the $bob$ is released from its horizontal position,then the speed of the $bob$ and the tension in the thread at the lowest position of the $bob$ will be respectively:

In the case of vertical circular motion of a particle attached to a thread of length $r$, if the tension in the thread is zero at an angle of $30^{\circ}$ with the horizontal as shown in the figure, the velocity at the bottom point $(A)$ of the circular path is ($g =$ gravitational acceleration).

$A$ stone of mass $900 \,g$ is tied to a string and moved in a vertical circle of radius $1 \,m$ making $10 \,rpm$. The tension in the string, when the stone is at the lowest point is (if $\pi^2=9.8$ and $g=9.8 \,m/s^2$): (in $\,N$)