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

$A$ small $100 \ g$ sleeve $B$ can slide on a smooth,circular and rigid wire frame $A$ of radius $5 \ m$ placed in a vertical plane. The wire frame is rotating about its vertical diameter at $2 \ rad/s$. When the sleeve is brought to a particular angular position $\theta$ (measured from the vertical downward axis) other than the bottom and the top of the ring,the sleeve will not slide on the wire frame. Calculate the normal force $N$ (in Newtons) of interaction between the sleeve and the wire frame at this position.

$A$ circular overbridge has a radius of $20\,m$. What is the maximum speed with which a car can cross the bridge without leaving contact with the overbridge at the highest point (in $,m/s$)? $(g = 9.8\,m/s^2)$

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 radius of curvature of the path of two particles of same masses are in the ratio $1 : 2$,then in order to have constant centripetal force,their velocity,should be in the ratio of

$A$ 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 $\,m/s$)?