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Two particles A, B are moving on two concentric circles of radii R₁ and R₂ with equal angular speed $ω$ . At t = 0, their positions and direction of motion are shown in the figure : The relative velocity ${\vec{υ}}_{A} - {\vec{υ}}_{B}$ at $t = \frac{π}{2 ω}$ is given by

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$ω (R_{1} - R_{2}) \hat{i}$

$ω (R_{2} - R_{1}) \hat{i}$

$ω (R_{1} + R_{2}) \hat{i}$

$- ω (R_{1} + R_{2}) \hat{i}$

answer is D.

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Detailed Solution

θ = ωt = ω(π/2ω) = 2π.
${\vec{V}}_{A} - \vec{V_{S}} = ω R_{1} {(- \hat{i})}_{} - ω R_{2} (- \hat{i})$

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