A circular disc of mass $2 \,kg$ and radius $10 \,cm$ rolls without slipping with a speed $2 \,m / s$. The total kinetic energy of disc is ………. $J$

Two uniform similar discs roll down two inclined planes of length $S$ and $2S$ respectively as shown is the fig. The velocities of two discs at the points $A$ and $B$ of the inclined planes are related as

A hoop of radius $2 \;m$ weighs $100\; kg$. It rolls along a horizontal floor so that its centre of mass has a speed of $20\; cm/s$. How much work has to be done to stop it?

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$. The value of $x$ is …………….

An air compressor is powered by a $200\,rad\,s^{-1}$ electric motor using a $V-$ belt drive. The motor pulley is $8\,cm$ in radius, and the tension in the $V-$ belt is $135\,N$ on one side and $45\,N$ on the other. The power of the motor will be …… $kW$.