Two particles A, B are moving|CIRCULAR MOTION|JEEMAIN 2019

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JEE MAIN 2019

12-01-2019 S2

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 $\vec{v}_A-\vec{v}_B$ at $t=\frac{\pi}{2 \omega}$ is given by

Select the correct option:

A

$\omega\left(R_2-R_1\right) \hat{i}$

B

$\omega\left(R_1-R_2\right) \hat{i}$

C

$-\omega\left(\mathrm{R}_1+\mathrm{R}_2\right) \hat{\mathrm{i}}$

D

$\omega\left(R_1+R_2\right) \hat{i}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} \omega t=\omega \frac{\pi}{2 \omega}=\frac{\pi}{2} \quad & \Rightarrow \overrightarrow{V_A}=\omega R_1(-\hat{i}) \\ \overrightarrow{V_B}=\omega R_2(-\hat{i}) & \Rightarrow \overrightarrow{V_A}=\overrightarrow{V_B}=\omega\left[R_2-R_1\right] \hat{i}\end{aligned}$

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