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