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 $^{\circ}$)

$A$ 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 $rad/s$)

In a circus,a stuntman rides a motorbike on a vertical circular track of radius $r$. Find the minimum speed he must maintain at the highest point of the track.

What is the minimum velocity at the lowest point of a vertical circle of radius $l$ such that the string just becomes slack at the highest point?

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

$A$ wire,which passes through the hole of a small bead,is bent in the form of a quarter of a circle. The wire is fixed vertically on the ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$,the force it applies on the wire is