An infinite number of spheres,each of mass $m$,are placed on the $X$-axis at distances $1, 2, 4, 8, 16, \dots$ meters from the origin. The magnitude of the gravitational field at the origin is

Two identical heavy spheres are separated by a distance $10$ times their radius. Will an object placed at the mid-point of the line joining their centres be in stable equilibrium or unstable equilibrium? Give reason for your answer.

$A$ uniform solid sphere of mass $m$ and radius $r$ is surrounded by a uniform thin spherical shell of radius $2r$ and mass $m$. Then the gravitational field:

$A$ spherical shell is cut into two pieces along a plane as shown in the figure. $P$ is a point on the plane of the cut. The gravitational field at $P$ due to the upper part is $I_1$ and that due to the lower part is $I_2$. What is the relation between them?

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.

Gravitational potential in a region is given by $V = -(x + y + z) \text{ J/kg}$. Find the gravitational intensity at $(2, 2, 2)$ in $\text{N/kg}$.