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]

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?

If the mass of a body is $M$ on the Earth's surface,then the mass of the same body on the Moon's surface is:

Two point masses $m$ and $4m$ are separated by a distance $d$ on a line. $A$ third point mass $m_0$ is to be placed at a point on the line such that the net gravitational force on it is zero. The distance of that point from the $m$ mass is:

Six point masses of mass $m$ each are at the vertices of a regular hexagon of side $l$. Calculate the net gravitational force on any one of the masses.

Find the acceleration of our galaxy due to the nearest comparably sized galaxy. The approximate mass of each galaxy is $8 \times 10^{11}$ solar masses,and they are separated by $2 \times 10^6$ light-years. Each galaxy has a diameter of $10^5$ light-years. (Assume $1 \text{ light-year} \approx 10^{16} \text{ m}$,gravitational constant $G \approx 10^{-10} \text{ Nm}^2/\text{kg}^2$,and mass of the Sun $= 2.0 \times 10^{30} \text{ kg}$)