Six objects are placed at the vertices of a regular hexagon. The geometric centre of the hexagon is at the origin with objects $1$ and $4$ on the $X$-axis (see figure). The mass of the $k$-th object is $m_k = k^i M |\cos \theta_k|$, where $i$ is an integer, $M$ is a constant with the dimension of mass, and $\theta_k$ is the angular position of the $k$-th vertex measured from the positive $X$-axis in the counter-clockwise sense. If the net gravitational force on a body at the centroid vanishes, the value of $i$ is

Gravitational mass is proportional to gravitational

Two concentric shells of masses $m_1$ and $m_2$ have radii $r_2$ and $r_1$ respectively (where $r_2 < r_1$). $A$ particle of mass $m$ is placed at positions $A, B,$ and $C$ as shown in the figure. The gravitational forces on the particle at these positions are:

Explain gravitational intensity.

$A$ 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.