Physics - Gravitation Question with Solution | TestHub

Consider a star of mass $m_2\mathrm{kg}$ revolving in a circular orbit around another star of mass $m_1\mathrm{kg}$ with $m_1\gg m_2$. The heavier star slowly acquires mass from the lighter star at a constant rate of $\gamma \mathrm{kg}/\mathrm{s}$. 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 $\frac{1}{r}\frac{\mathrm{d}r}{\mathrm{d}t}($ in s ${}^{-1})$ is given by: [Note: The original question was awarded bonus marks in the JEE Advanced 2025 exam. We have changed the options to make the question valid and solvable.]