The gravitational field in a region is given by $I = (5 \hat{i} + 12 \hat{j}) \text{ N kg}^{-1}$. The change in the gravitational potential energy of an object of mass $3 \text{ kg}$ when it is taken from the origin to a point $(8 \text{ m}, -2 \text{ m})$ is (in $\text{ J}$)

If the distance between the centres of Earth and Moon is $D$ and the mass of Earth is $81$ times that of the Moon,at what distance from the centre of Earth will the gravitational field be zero?

The gravitational field,due to the 'left over part' of a uniform sphere (from which a part as shown,has been 'removed out'),at a very far off point,$P$,located as shown,would be (nearly)

Two point masses having mass $m$ and $2m$ are placed at a distance $d$. The point on the line joining the point masses,where the gravitational field intensity is zero,will be at a distance ............

$A$ mass $m$ is placed at point $P$ on the axis of a ring of mass $M$ and radius $R$ at a distance $R$ from its centre. The gravitational force on mass $m$ is

This question contains Statement-$1$ and Statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
Statement-$1$: For a mass $M$ kept at the centre of a cube of side '$a$',the flux of the gravitational field passing through its sides is $-4\pi GM$.
Statement-$2$: If the direction of a field due to a point source is radial and its dependence on the distance '$r$' from the source is given as $\frac{1}{r^2}$,its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.