If two identical spherical bodies of same material and dimensions are kept in contact,the gravitational force between them is proportional to $R^{x}$,where $x$ is a non-zero integer. [Given: $R$ is the radius of each spherical body]

$A$ 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 $= 1.5 \times 10^{11} \; m$)

$A$ point mass '$m$' is located at a distance '$r$' from the end of a uniform thin rod of mass '$M$' and length '$L$' as shown in the figure. The magnitude of the gravitational force of attraction is

Two stars of masses $m_1$ and $m_2$ are parts of a binary star system. The radii of their orbits are $r_1$ and $r_2$ respectively,measured from the centre of mass of the system. The magnitude of the gravitational force that $m_1$ exerts on $m_2$ is

Two particles of equal mass $m$ move in a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle 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.