Gravity cancellation point [closed]

Here is a question from ANTHE: an exam in India. The question is:
Two point masses M and 3M are placed at a L distance apart. Another point mass m is between on the line joining them so that the net gravitational force acting on it due to masses M and 3M is zero. The magnitude of gravitational force acting on m due to M will be? (Please answer in terms of variables!)
This question looked for me as the same lagrange point between sun and earth.
• nope! Lagrange points are based on equilibrium in a rotating frame where in addition to real gravitational potential energy, you also include a fictitious rotational pseudopotential that accounts for the apparent behavior of real rotational effects as they appear in the rotating frame. You can not argue that your problem is a special case for Lagrange points where rotation goes to zero because there must be a finite rotation speed that keeps $M$ and $3M$ in orbit around their center of mass. So better avoid thinking about rotation for your physics problem. – uhoh Oct 20 '18 at 12:16