$A$ gravitational field is present in a region and a mass is shifted from $A$ to $B$ through different paths as shown. If $W_1, W_2$ and $W_3$ represent the work done by the gravitational force along the respective paths,then

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 $= 2.0 \times 10^{30} \text{ kg}$)

$A$ 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:

Define the universal gravitational constant $(G)$.

We can shield a charge from electric fields by putting it inside a hollow conductor. Can we shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?

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?