$A$ motorcycle is moving on an overbridge of radius $R$. The driver maintains a constant speed $v$. As the motorcycle is ascending on the overbridge,the normal force on it is

$A$ particle describes a horizontal circle in a conical funnel whose inner surface is smooth with a speed of $0.5 \, m/s$. What is the height of the plane of the circle from the vertex of the funnel in $cm$?

$A$ mass of $100\, g$ is tied to one end of a string $2\, m$ long. The body is revolving in a horizontal circle making a maximum of $200$ revolutions per minute. The other end of the string is fixed at the center of the circle of revolution. The maximum tension that the string can bear is .......... $N$ (approximately).

An object of mass $m$ moves with constant speed in a circular path of radius $R$ under the action of a force of constant magnitude $F$. The kinetic energy of the object is ............

$A$ smooth wire of length $2\pi r$ is bent into a circle and kept in a vertical plane. $A$ bead can slide smoothly on the wire. When the circle is rotating with angular speed $\omega$ about the vertical diameter $AB$,as shown in the figure,the bead is at rest with respect to the circular ring at position $P$ as shown. Then the value of $\omega^2$ is equal to

$A$ car of mass $m$ passes over the top of a convex bridge of radius of curvature $r$ with a velocity $v$. What is the normal force exerted by the bridge on the car?