$A$ mass $M$ is divided into two parts $xM$ and $(1 - x)M$. For what value of $x$ is the gravitational force between them maximum for a given distance?

Two masses $m_1$ and $m_2$ $(m_1 < m_2)$ are released from rest from a finite distance. They start moving under their mutual gravitational attraction.

Which of the following is incorrect about the gravitational force between two bodies?

From a sphere of mass $M$ and radius $R$,a smaller sphere of radius $\frac{R}{2}$ is carved out. For the configuration shown in the figure where the distance between the center of the original sphere and the center of the removed sphere is $3R$,the gravitational force between the two spheres is:

Are the inertial mass and gravitational mass of a body different from each other?

Two particles each of mass $m$ are placed at points $P$ and $Q$ as shown in the figure. $R$ is the mid-point of $PQ = l$. The gravitational force on the third particle of mass $m$ placed at point $S$ on the perpendicular bisector of $PQ$ is