$A$ cyclist goes round a circular path of circumference $34.3 \ m$ in $\sqrt{22} \ s$. The angle made by him with the vertical will be ....... $^o$.

If a stone of mass $0.5 \ kg$ tied to one end of a wire is whirled in a circular path of radius $2 \ m$ with a speed $40 \ rev/min$ in a horizontal plane,then the tension in the wire is nearly (in $N$)

$A$ particle of mass '$m$' is rotating along a circular path of radius '$r$' having angular momentum '$L$'. The centripetal force acting on the particle is given by

$A$ particle of mass $M$ moves with constant speed along a circular path of radius $r$ under the action of a force $F$. Its speed is

$A$ dancer moves counterclockwise at a constant speed around the path shown below. The path is such that the lengths of its segments,$PQ, QR, RS$,and $SP$,are equal. Arcs $QR$ and $SP$ are semicircles. Which of the following best represents the magnitude of the dancer's acceleration as a function of time $t$ during one trip around the path,beginning at point $P$?

$A$ particle of mass $m$ is suspended from a ceiling through a string of length $L$. If the particle moves in a horizontal circle of radius $r$ as shown in the figure,then the speed of the particle is