$A$ 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

$A$ mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity $\omega_0$. If the length of the string and angular velocity are doubled,the tension in the string which was initially $T_0$ is now

$A$ 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

$A$ 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 moves in a horizontal circle on the smooth inner surface of a hemispherical bowl of radius $R$. The plane of motion is at a depth $d$ below the centre of the hemisphere. The speed of the particle is:

$A$ particle rotates in a horizontal circle of radius $r$ in a conical funnel with speed $v$. The inner surface of the funnel is smooth. The height $h$ of the plane of the circle from the vertex of the funnel is (where $g$ is the acceleration due to gravity):