A object mass m is sliding freely on a frictionless surface table and is connected by a tight cable (with neglected mass) to a mass M that hangs below (see the figure). Be award that M is moving in a vertical line only. (Hint take v=0 at the table surface, the cable always remains tight - not flexible). Use the generalized shown in the figure, the lagragian of the system can be given as \begin{align*} \frac{1}{2}m\dot{r}^2 + \frac{1}{2}m(r\dot{\theta})^2 + Mg(l-r) \\ \frac{1}{2}M\dot{r}^2 + \frac{1}{2}m(r\dot{\theta})^2 + Mg(r) \\ \frac{1}{2}m\dot{r}^2 + \frac{1}{2}m(r\dot{\theta})^2 + Mg(l-r) \\ \frac{1}{2}m\dot{r}^2 + \frac{1}{2}m(r\dot{\theta})^2 - Mg(l-r) \\ \frac{1}{2}M\dot{r}^2 + \frac{1}{2}m(r\dot{\theta})^2 - Mg(l-r) \end{align*}
