For circular motion, if ${\vec a_t},\,{\vec a_c},\,\vec r$ and $\vec v$ are tangential acceleration, centripetal acceleration, radius vector and velocitym respectively, then find the wrong relation

Two particles $A$ and $B$ start at the origin $O$ and travel in opposite directions along the circular path at constant speeds $0.5\,m/s$ and $1.5\,m/s$ , respectively. The time when they collide with each other ........ $\sec$

A huge circular arc of length $4.4$ $ly$ subtends an angle $'4 {s}'$ at the centre of the circle. How long it would take for a body to complete $4$ revolution if its speed is $8 \;AU\;per\, second \;?$

Given : $1\, {ly}=9.46 \times 10^{15} \,{m},$ $\, {AU}=1.5 \times 10^{11}\, {m}$

A particle moves in a circular path of radius $R$ with an angular velocity $\omega = a -bt$ where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $\frac {2a}{b}$ is

For a particle in uniform circular motion, the acceleration $\vec a$ at a point $P(R,\theta)$ on the circle of radius $R$ is (Here $\theta$ is measured from the $x-$ axis)

The angular speed of earth around its own axis is ......... $rad / s$