In a circus,a stuntman rides a motorbike on a circular track of radius $R$ in the vertical plane. The minimum speed at the highest point of the track will be:

The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the string. The angular amplitude of the pendulum is (in $^{\circ}$)

$A$ stone of mass $2 \,kg$ tied to a light inextensible string of length $\frac{5}{3} \,m$ is whirling in a circular path in a vertical plane. If the ratio of the maximum tension to the minimum tension in the string is $4$, then the speed of the stone at the highest point of the circle is $\left(g=10 \,ms^{-2}\right)$.

$A$ body of mass $m$ connected to a massless and unstretchable string moves in a vertical circle of radius $R$ under gravity $g$. The other end of the string is fixed at the center of the circle. If the velocity at the top of the circular path is $n\sqrt{gR}$,where $n \geq 1$,then the ratio of the kinetic energy of the body at the bottom to that at the top of the circle is:

$A$ $2 \, kg$ stone at the end of a string $1 \, m$ long is whirled in a vertical circle at a constant speed. The speed of the stone is $4 \, m/s$. The tension in the string will be $52 \, N$ when the stone is:

$A$ body slides down a frictionless track which ends in a circular loop of diameter $D$. The minimum height $h$ of the body in terms of $D$ so that it may just complete the loop is: