$A$ $2 \, kg$ 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 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:

$A$ small bob tied at one end of a thin string of length $1\, m$ is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio $5: 1$. The velocity of the bob at the highest position is ............. $m/s$ (Take $g=10\, m/s^2$).

$A$ 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 ......... $N$.

$A$ body of mass $100 \ g$ is moving in a circular path of radius $2 \ m$ on a vertical plane as shown in the figure. The velocity of the body at point $A$ is $10 \ m/s$. The ratio of its kinetic energies at point $B$ and $C$ is: (Take acceleration due to gravity as $10 \ m/s^2$)

$A$ pendulum consisting of a small sphere of mass $m$ suspended by an inextensible and massless string of length $l$ is made to swing in a vertical plane. If the breaking strength of the string is $2mg$,then the maximum angular amplitude of the displacement from the vertical can be ....... $^o$