$A$ table rotates about a vertical axis passing through its center with an angular velocity of $20\ rad/s$. $A$ flywheel is mounted on it,which rotates about a horizontal axis with an angular velocity of $40\ rad/s$. The resultant angular velocity of the flywheel is:

In the following figure,a body of mass $m$ is tied at one end of a light string and this string is wrapped around a solid cylinder of mass $M$ and radius $R$. At the moment $t = 0$,the system starts moving. If the friction is negligible,the angular velocity at time $t$ would be

Two masses $m$ and $2m$ are connected by a light string passing over a pulley (disc) of mass $M = 30m$ and radius $r = 0.1 \ m$. The pulley is mounted in a vertical plane and is free to rotate about its axis. The $2m$ mass is released from rest. Find its speed when it has descended through a height of $h = 3.6 \ m$. (Assume the string does not slip and $g = 10 \ m/s^2$)

$A$ mass $m$ is supported by a massless string wound around a uniform hollow cylinder of mass $m$ and radius $R$. If the string does not slip on the cylinder,then with what acceleration will the mass be released? (Assume $g =$ acceleration due to gravity)

$A$ solid body rotates about a fixed axis such that its angular velocity depends on $\theta$ as $\omega = k \theta^{-1}$,where $k$ is a positive constant. At $t = 0$,$\theta = 0$. Then,the time dependence of $\theta$ is given as ..........

$A$ sphere is rotating about a diameter.