The force of mutual attraction between any two objects by virtue of their masses is

Two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to ($R =$ radius of each sphere).

The gravitational force between a hollow spherical shell (of radius $R$ and uniform density) and a point mass $m$ is $F$. Show the nature of the $F$ versus $r$ graph,where $r$ is the distance of the point mass from the centre of the hollow spherical shell.

The distance between the centre of the moon and the earth is $D$ and 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 an object be zero?

The distance between two objects $A$ and $B$ is $r$. The gravitational force between them is inversely proportional to the square of the distance. If the gravitational force between these two objects were inversely proportional to the fourth power of the distance,find the acceleration of object $A$.

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?