Consider a star of mass \(m_2 kg\) revolving in a circular orbit around another star of mass \(m_1 kg\) with \(m_1 \gg m…

Consider a star of mass \(m_2 kg\) revolving in a circular orbit around another star of mass \(m_1 kg\) with \(m_1 \gg m_2\). The heavier star slowly acquires mass from the lighter star at a constant rate of \(\gamma kg / s\). In this transfer process, there is no other loss of mass. If the separation between the centers of the stars is \(r\), then its relative rate of change \(\frac{1}{r} \frac{d r}{d t}\) (in \(s ^{-1}\) ) is given by:

[JEE Advanced 2025]