Moment of inertia of a body about a given axis is $1.5\, kg\, m^2$ Initially the body is at rest. In order to produce a rotational kinetic energy of $1200\, J$, the angular acceleration of $20\, rad/s^2$ must be applied about the axis of rotation for a duration of ......... $\sec$.

A circular disc of mass $M$ and radius $R$ is rotating about its axis with angular speed $\omega_{1}$ If another stationary disc having radius $\frac{ R }{2}$ and same mass $M$ is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed $\omega_{2}$. The energy lost in the process is $p \%$ of the initial energy. Value of $p$ is

As shown in the figure, a bob of mass $\mathrm{m}$ is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius $\mathrm{r}$ and mass $m$. When released from rest the bob starts falling vertically. When it has covered a distance of $h$. the angular speed of the wheel will be

Part of the tuning arrangement of a radio consists of a wheel which is acted on by two parallel constant forces as shown in the fig. If the wheel rotates just once, the work done will be about (diameter of the wheel = $0.05\ m$)

A particle performs uniform circular motion with an angular momentum $L.$  If the angular frequency of the particle is doubled and kinetic energy is halved, its angular momentum becomes

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of $\theta ,$ where $\theta $ is the angle by which it has rotated, is given as $k\theta ^2.$ If its moment of inertia is $I$ then the angular acceleration of the disc is