Assuming the motion of Earth around the Sun as a circular orbit with a constant speed of $30 \mathrm{km} {\mathrm{h}}^{-1}$.

A ball of mass $\left(m\right) 0.5 \mathrm{kg}$ is attached to the end of a string having length $\left(L\right) 0.5 \mathrm{m}$. The ball is rotated on a horizontal circular path about a vertical axis. The maximum tension that the string can bear is $324 \mathrm{N}$. The maximum possible value of the angular velocity of ball (in $\mathrm{rad} {\mathrm{s}}^{-1}$) is :

Two identical discs of the same radius $R$ are rotating about their axes in opposite directions with the same constant angular speed $\omega$. The disc is in the same horizontal plane.At time $t\mathit{ }= 0$, the points $P$ and $Q$ are facing each other as shown in the figure. The relative speed between the two points $P$ and $Q$ is $v_{\mathit{r}}$ as a function of times best represented by