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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीIn a binary star system, two stars of masses \( m_1 \) and \( m_2 \) separated by distance \( d \) rotate in circular orbits around their common centre of mass under their mutual gravitational attraction. If \( r_1 \) and \( r_2 \) are the radii of their orbits and \( v_1 \) and \( v_2 \) are their respective orbital speeds, which of the following relations is correct?
Correct answer · Option 2
\( \frac{v_1}{v_2} = \frac{m_2}{m_1} \)
Explanation
Since the centre of mass is at rest, \( m_1 r_1 = m_2 r_2 \implies \frac{r_1}{r_2} = \frac{m_2}{m_1} \). Both stars have the identical angular velocity \( \omega \), so \( \frac{v_1}{v_2} = \frac{\omega r_1}{\omega r_2} = \frac{r_1}{r_2} = \frac{m_2}{m_1} \).
