A particle moves along a horizontal circle such that the radial force acting on it is directly proportional to square of time. Then choose the correct option :

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

A point $P$ moves in a counter-clockwise direction on a circular path as shown in the figure. The movement of $\mathit{‘}P\mathit{’}$ is such that it sweeps out a length $s=t^3+5$, where $s$ is in meters and $t$ is in seconds. The radius of the path is $20 \mathrm{m}$. The acceleration of $‘P’$ when $t=2 \mathrm{s}$ is nearly