$A$ mass $M$ at rest is broken into two pieces having masses $m$ and $(M-m)$. The two masses are then separated by a distance $r$. The gravitational force between them will be maximum when the ratio of the masses $[m : (M-m)]$ of the two parts is:

$A$ rocket is fired from the Earth towards the Sun. At what distance from the Earth's centre is the gravitational force on the rocket zero? Mass of the Sun $= 2 \times 10^{30} \; kg$,mass of the Earth $= 6 \times 10^{24} \; kg$. Neglect the effect of other planets,etc. (Orbital radius $= 1.5 \times 10^{11} \; m$)

Two identical spheres each of radius $r$ are placed in contact with each other. Show that the gravitational force between them is proportional to $r^4$.

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

Draw a schematic diagram of Cavendish's experiment for the determination of the universal gravitational constant $G$ and obtain the formula used in it.

Three particles $A, B$ and $C$ each of mass $m$ are lying at the corners of an equilateral triangle of side $L$. If the particle $A$ is released keeping the particles $B$ and $C$ fixed,the magnitude of instantaneous acceleration of $A$ is ........