The gravitational force $F_g$ between two objects does not depend on

$A$ mass $M$ is split into two parts,$m$ and $(M-m)$,which are then separated by a certain distance. What ratio of $\frac{m}{M}$ maximizes the gravitational force between the two parts?

Mass $M$ is divided into two parts $xM$ and $(1-x)M$. For a given separation,the value of $x$ for which the gravitational attraction between the two pieces becomes maximum is

Find the acceleration of our galaxy due to the nearest comparably sized galaxy. The approximate mass of each galaxy is $8 \times 10^{11}$ solar masses,and they are separated by $2 \times 10^6$ light-years. Each galaxy has a diameter of $10^5$ light-years. (Assume $1 \text{ light-year} \approx 10^{16} \text{ m}$,gravitational constant $G \approx 10^{-10} \text{ Nm}^2/\text{kg}^2$,and mass of the Sun $= 2.0 \times 10^{30} \text{ kg}$)

Two objects of equal masses placed at a certain distance from each other attract each other with a force of $F$. If one-third mass of one object is transferred to the other object,then the new force will be

Which of the following statements about the gravitational constant $G$ is true?