The gravitational force between two identical uniform solid gold spheres of radius $r$ placed in contact is proportional to:

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?

The mass of the Moon is approximately $10\%$ of the mass of the Earth. What will be the gravitational force exerted by the Moon on the Earth compared to the gravitational force exerted by the Earth on the Moon?

$A$ 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?

$A$ uniform sphere of mass $M$ and radius $R$ is surrounded by a concentric spherical shell of the same mass but radius $2R$. $A$ point mass $m$ is kept at a distance $x$ $(R < x < 2R)$ in the region bounded by the spheres as shown in the figure. The net gravitational force on the particle is:

The distance between the centres of the moon and the earth is $D$. The mass of the earth is $81$ times the mass of the moon. At what distance from the centre of the earth will the net gravitational force on a test mass be zero?