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 :
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 :
The relative velocity \(\vec V_A-\vec V_B\) at \(t=\frac{\pi}{2\omega}\) is given by :
Show Hint
From the figure A (inner circle, radius \(R_1\)) goes anticlockwise and B (outer circle, radius \(R_2\)) goes clockwise. At \(t=\frac{\pi}{2\omega}\) each has turned through \(90^\circ\).
Updated On: Nov 5, 2026
- \(-\omega(R_1+R_2)\,\hat i\)
- \(\omega(R_2-R_1)\,\hat i\)
- \(\omega(R_1+R_2)\,\hat i\)
- \(\omega(R_1-R_1)\,\hat i\)
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The Correct Option is B
Solution and Explanation
Figure: at t = 0, A is at \((R_1,0)\) moving up (+y), so it moves anticlockwise; B is at \((R_2,0)\) moving down (-y), so it moves clockwise.
Angle turned by each in \(t=\frac{\pi}{2\omega}\): \(\omega t=\frac{\pi}{2}\).
A is now at \((0,R_1)\) (top of its circle); anticlockwise motion at the top is towards -x: \(\vec v_A=-\omega R_1\,\hat i\).
B is now at \((0,-R_2)\) (bottom of its circle); clockwise motion at the bottom is towards -x: \(\vec v_B=-\omega R_2\,\hat i\).
\(\vec v_A-\vec v_B=-\omega R_1\,\hat i+\omega R_2\,\hat i=\omega(R_2-R_1)\,\hat i\).
Answer: (2) \(\omega(R_2-R_1)\,\hat i\)
Angle turned by each in \(t=\frac{\pi}{2\omega}\): \(\omega t=\frac{\pi}{2}\).
A is now at \((0,R_1)\) (top of its circle); anticlockwise motion at the top is towards -x: \(\vec v_A=-\omega R_1\,\hat i\).
B is now at \((0,-R_2)\) (bottom of its circle); clockwise motion at the bottom is towards -x: \(\vec v_B=-\omega R_2\,\hat i\).
\(\vec v_A-\vec v_B=-\omega R_1\,\hat i+\omega R_2\,\hat i=\omega(R_2-R_1)\,\hat i\).
Answer: (2) \(\omega(R_2-R_1)\,\hat i\)
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