$A$ point mass '$m$' is moved in a vertical circle of radius '$r$' with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point is .......... $mg$.

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).

$A$ particle is tied to a $20 \ cm$ long string. It performs circular motion in a vertical plane. What is the angular speed of the particle when the tension in the string at the top is zero? (Take $g = 9.8 \ m/s^2$)

$A$ stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

$A$ small cube with mass $M$ starts at rest at point $1$ at a height $4R$,where $R$ is the radius of the circular part of the track. The cube slides down the frictionless track and around the loop. The force that the track exerts on the cube at point $2$ is nearly ......... times the cube's weight $mg$.

$A$ weightless thread can bear tension 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. The maximum angular velocity of the stone will be (acceleration due to gravity,$g = 10 \ m/s^2$) (in $rad/s$)