$A$ coin placed on a rotating turntable just slips if it is placed at a distance of $4 \ cm$ from the centre. If the angular velocity of the turntable is doubled,it will just slip at a distance of: (in $cm$)

$A$ 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

$A$ string of length $L$ fixed at one end carries a body of mass $m$ at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string makes an angle $\theta$ with the vertical. The angular frequency of the body is $\omega$. The tension in the string is

An aircraft executes a horizontal loop at a speed of $720 \; km/h$ with its wings banked at $15^{\circ}$. What is the radius of the loop in $km$?

If the radii of circular paths of two particles of same mass are in the ratio of $1: 2$, then to have a constant centripetal force, the ratio of their speeds should be

$A$ string of length $0.1\,m$ cannot bear a tension more than $100\,N$. It is tied to a body of mass $100\,g$ and rotated in a horizontal circle. The maximum angular velocity can be .......... $rad/s$.