question_answer

Two particles A, B are moving on two concentric circles of radii \[{{R}_{1}}\]and \[{{R}_{2}}\]with equal angular speed co. At t = 0, their positions and direction of motion are shown in the figure:

The relative velocity \[{{\overrightarrow{v}}_{A}}-{{\overrightarrow{v}}_{B}}\]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) \[\omega ({{R}_{2}}-{{R}_{1}})\hat{i}\]           

D) \[\omega ({{R}_{1}}-{{R}_{2}})\hat{i}\]           

Correct Answer: C

Solution :

At \[t=0\]

At         \[t=\frac{\pi }{2\omega }\]

\[{{\vec{\nu }}_{A}}-{{\overrightarrow{v}}_{B}}=-\omega {{R}_{i}}\hat{i}+\omega .{{R}_{2}}\hat{i}\]\[=\omega ({{R}_{2}}-{{R}_{1}})\hat{i}.\]