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 $\overset{ \rightarrow }{V_{A}}-\overset{ \rightarrow }{V_{B}}$ at $t=\frac{\pi }{2 \omega }$ is given by:

• A. $-\omega \left(R_{1} + R_{2}\right)\hat{i}$
• B. $\omega \left(R_{1} + R_{2}\right)\hat{i}$
• C. $\omega \left(R_{1} - R_{2}\right)\hat{i}$
• D. $\omega \left(R_{2} - R_{1}\right)\hat{i}$

Answer 1

Answer: (D)

$t=\frac{\pi }{2 \omega }$

$\left(\overset{ \rightarrow }{V}\right)_{A}=\omega R_{1}\left(- \hat{i}\right)$
$\left(\overset{ \rightarrow }{V}\right)_{B}=\omega R_{2}\left(- \hat{i}\right)$
$\overset{ \rightarrow }{V_{A}}-\overset{ \rightarrow }{V_{B}}=\omega \left(R_{2} - R_{1}\right)\hat{i}$