Question

Two particles $A,B$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega$. At $t=0$, their positions and direction of motion are shown in the figure:
The relative velocity ${\overrightarrow{u}}_A-{\overrightarrow{v}}_B$ at $t=\frac{\pi }{2\omega }$ is given by:

• A. $-\omega (R_1+R_2)\hat{i}$
• B. $\omega (R_1+R_2)\hat{i}$
• C. $\omega (R_1-R_2)\hat{i}$
• D. $\omega (R_2-R_1)\hat{i}$

Answer 1

The correct option is D $\omega (R_2-R_1)\hat{i}$

$\theta =\omega t=\omega \frac{\pi }{2\omega }=\frac{\pi }{2}$.
${\overrightarrow{V}}_A-\overrightarrow{V}S=\omega R_1(-\hat{i})-\omega R_2(-i)$