Consider an infinite distribution of point masses (each of mass $m$) placed on the $x$-axis as shown in the diagram. What is the gravitational force acting on the point mass placed at the origin?

Two point masses $A$ and $B$ having masses in the ratio $4 : 3$ are separated by a distance of $1\, m$. When another point mass $C$ of mass $M$ is placed in between $A$ and $B$,the gravitational force between $A$ and $C$ is $\frac{1}{3}$ of the gravitational force between $B$ and $C$. Then the distance of $C$ from $A$ is:

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$. The space around the masses is now filled with a liquid of specific gravity $3$. The gravitational force between the bodies will now be

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 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?

$A$ gravitational field is present in a region and a mass is shifted from $A$ to $B$ through different paths as shown. If $W_1, W_2$ and $W_3$ represent the work done by the gravitational force along the respective paths,then