Consider a particle moving with a minimum speed $v$ at the highest point of a vertical circle of radius $R$. If the radius of the circle is doubled, the corresponding minimum speed will be:

$A$ bob of mass $M$ is suspended by a massless string of length $L$. The horizontal velocity $V$ at position $A$ is just sufficient to make it reach the point $B$. The angle $\theta$ at which the speed of the bob is half of that at $A$, satisfies:

$A$ heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:

$A$ particle is rotated in a vertical circle by connecting it to a light rod of length $l$ and keeping the other end of the rod fixed. The minimum speed of the particle when the light rod is horizontal for which the particle will complete the circle is

$A$ mass is performing vertical circular motion (see figure). If the average velocity of the particle is increased,then at which point will the string break?

$A$ weightless thread can bear a tension of up to $3.7 \, kg \, wt$. $A$ stone of mass $500 \, g$ is tied to it and revolved in a circular path of radius $4 \, m$ in a vertical plane. If $g = 10 \, m/s^2$,then the maximum angular velocity of the stone will be ........ $rad/s$.