$A$ cyclist riding a bicycle at a speed of $14\sqrt{3} \text{ m/s}$ takes a turn around a circular road of radius $20\sqrt{3} \text{ m}$ without skidding. Given $g = 9.8 \text{ m/s}^2$,what is his inclination to the vertical in degrees?

$A$ bob of mass $m$ is whirled in a horizontal plane by means of a string of length $\ell$ with an initial angular speed of $\omega$. The tension in the string is $T$. If the angular speed becomes $2\omega$ while keeping the same radius $\ell$,the tension in the string becomes:

Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius of $(r/3)$ and the lighter one in a radius of $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is:

$A$ particle of mass $m$ is moving in a circular path of radius $r$ in a plane. Its angular momentum is $L$. The value of the centripetal force acting on the particle is:

$A$ coin,placed on a rotating turntable,slips when it is placed at a distance of $9 \, cm$ from the center. If the angular velocity of the turntable is tripled,it will just slip if its distance from the center is ......... $cm$.

$A$ 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