Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F.$ The space around the masses is now filled with a liquid of specific gravity $3.$ The gravitational force will now be

$A$ 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

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

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

Two particles each of mass $m$ are placed at points $P$ and $Q$ as shown in the figure. $R$ is the mid-point of $PQ = l$. The gravitational force on the third particle of mass $m$ placed at point $S$ on the perpendicular bisector of $PQ$ is

The gravitational force between two identical uniform solid gold spheres of radius $r$ placed in contact is proportional to: