Two particles A, B are moving on two concentric circles of radii R1… | JEE Main 2019 (12 Jan, Shift 2)

Q63JEE Main 2019 · 12 JAN · SHIFT 2Difficult

Angular Momentum & its Conservation

Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed $\omega$ . At t = 0, their positions and direction of motion are shown in the figure.:

The relative velocity $\vec{V}_A - \vec{V}_B$ at t = $\frac{\pi}{2\omega}$ is given by:

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Answer: (b)

A moves anticlockwise, B moves clockwise; in time $t = \frac{\pi}{2\omega}$ each turns through $90^\circ$ .
A reaches $(0, R_1)$ ; anticlockwise motion there is along $-\hat{i}$ : $\vec{V}_A = -\omega R_1\hat{i}$ .
B reaches $(0, -R_2)$ ; clockwise motion there is also along $-\hat{i}$ : $\vec{V}_B = -\omega R_2\hat{i}$ .
$\vec{V}_A - \vec{V}_B = \omega(R_2 - R_1)\hat{i}$
So the answer is (b) $\omega(R_2-R_1)\hat{i}$ .

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