$A$ 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?

$A$ particle moves with constant angular velocity in a circular path of a certain radius and is acted upon by a certain centripetal force $F$. If the angular velocity is kept the same but the radius of the path is halved,the new force will be

$A$ roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is $20\, m$. The speed of the car at the top of the hill is between

$A$ ball of mass $0.25 \,kg$ attached to the end of a string of length $1.96 \,m$ is moving in a horizontal circle. The string will break if the tension is more than $25 \,N$. What is the maximum speed with which the ball can be moved (in $\,m/s$)?

$A$ conical pendulum is moving in a circle with angular velocity $\omega$ as shown. If the tension in the string is $T$,which of the following equations is correct?

$A$ particle describes a horizontal circle of radius $r$ in a conical funnel with a smooth inner surface with a speed of $v = 0.5 \text{ m/s}$. The height $h$ of the plane of the circle from the vertex of the funnel is (acceleration due to gravity, $g = 10 \text{ m/s}^2$): (in $\text{ cm}$)