Question

Speed of a particle moving in a circle of radius $2$m varies with time as $v=2t$ (SI units). At $t=1s$ match the following two columns.
Here. symbols have their usual meanings.

Answer 1

(A)tangential acceleration is$2m/s^2$
centripetal acceleration is $v^2/R=4/2=2$
Now$\overrightarrow{a}.\overrightarrow{v}=avcos\theta =a_{tangential}v=4$
A->3
(B)$\omega$ is perpendicular to the plane of motion therefore, $\overrightarrow{a}\times \overrightarrow{\omega }=a\omega =2\sqrt{2}\times v/R=2\sqrt{2}$
B->1
(C) $\overrightarrow{v}.\overrightarrow{\omega }=0$ because v is perpendicular to $\omega$
C->4
(D) $\overrightarrow{v}\times \overrightarrow{a}=va\sin \theta =v{a}_{centripetal}=2\times 2=4$
D->3