$A$ mass $M$ is divided into two parts $xM$ and $(1 - x)M$. For a given separation,the value of $x$ for which the gravitational attraction between the two pieces becomes maximum is

$A$ 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 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?

How much force of gravitation acts on a body at an infinite distance from the Earth?

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.

Two identical particles each of mass $m$ go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be