$A$ body is placed as shown in the figure. To complete one full vertical circular loop,the height $h$ must be:

$A$ body tied to a string of length $L$ is revolved in a vertical circle with minimum velocity. When the body reaches the uppermost point,the string breaks and the body moves under the influence of the gravitational field of the Earth along a parabolic path. The horizontal range $AC$ of the body will be

$A$ 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 $\left(g=10 \,ms^{-2}\right)$.

$A$ stone of mass $1 \ kg$ tied to a light inextensible string of length $L = \frac{5}{3} \ m$ is rotating in a circular path of radius $L$ in a vertical plane. If the ratio of maximum tension in the string to the minimum tension in the string is $3$,the speed of the stone at the highest point of the circle is ($g =$ acceleration due to gravity).

In order to just complete the vertical circular motion,the ratio of kinetic energy of a particle at the highest point to that at the lowest point is

$A$ smooth inclined plane ends in a vertical circular loop, as shown in the figure. $A$ small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of the circle, then the height $h = \alpha R$. The value of $\alpha$ is . . . . . . .