7 questions
Consider a star of mass \( m_{2} \) \( \text{kg} \) revolving in a circular orbit around another star of mass \( m_{1} \) \( \text{kg} \) with \( m_{1} \gg m_{2} \). The heavier star slowly acquires mass from the lighter star at a constant rate of \( \gamma \) \( \text{kg/s} \). In this transfer process, there is not other loss of mass. If the separation between the centres of the stars is \( r \), then its relative rate of change \( \dfrac{1}{r}\dfrac{dr}{dt} \) (in \( \text{s}^{-1} \)) is given by:
A particle of mass \(m\), and angular momentum \(l\) is moving in a circular orbit of radius \(r_{0}\) under the influence of an attractive force \( \vec{F}(r) = - \dfrac{k}{r^{2}} \, \hat{r} \). Keeping its angular momentum unchanged, the particle is displaced radially by small distance \(\delta r \ll r_{0}\), due to which its radial distance varies periodically.
The corresponding time period is:
