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:

If the mass of two bodies is doubled and the distance between them is also doubled,what happens to the new gravitational force?

$A$ straight rod of length $L$ extends from $x = a$ to $x = L + a$. The gravitational force it exerts on a point mass $m$ at $x = 0$,if the mass per unit length of the rod is $A + Bx^2$,is given by

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

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.