$A$ mass $M$ at rest is broken into two pieces having masses $m$ and $(M-m)$. The two masses are then separated by a distance $r$. The gravitational force between them will be maximum when the ratio of the masses $[m : (M-m)]$ of the two parts is:

Statement $(I)$: The force of attraction due to a hollow spherical shell of uniform density on a point mass situated inside it is always zero.
Statement $(II)$: The force of attraction between a hollow spherical shell of uniform density and a point mass situated outside is the same as if the entire mass of the shell were concentrated at the center of the shell.
Which of the following is correct?

Two bodies of masses $8 \,kg$ are placed at the vertices $A$ and $B$ of an equilateral triangle $ABC$. $A$ third body of mass $2 \,kg$ is placed at the centroid $G$ of the triangle. If $AG=BG=CG=1 \,m$, where should a fourth body of mass $4 \,kg$ be placed, so that the resultant force on the $2 \,kg$ body is zero?

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.

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will:

If the mass of a body is $M$ on the Earth's surface,then the mass of the same body on the Moon's surface is: