Three equal masses of $m$ are placed at the vertices of an equilateral triangle ABC. Let the distanc

Question

Three equal masses of $m$ are placed at the vertices of an equilateral triangle ABC. Let the distance from the centroid G to each vertex be $r$. A mass $2m$ is placed at G. If the mass at A is doubled to $2m$, what is the net gravitational force acting on the mass at G?

Professor PC Thomas Classes · Answer

Initially, the net force is zero. When the mass at A is doubled to $2m$, it is equivalent to adding an extra mass $m$ at A. The net force is solely due to this additional mass $m$ acting on $2m$ at G. $F = \frac{G(m)(2m)}{r^2} = \frac{2G m^2}{r^2}$ directed towards A.