Gauss's law for gravitation is given by:

Two concentric spherical shells have masses $M_1$ and $M_2$ and radii $r_1$ and $r_2$ $(r_1 < r_2)$. What is the gravitational intensity at a distance $r$ from the center where $r_1 < r < r_2$?

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

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

$3$ particles each of mass $m$ are kept at the vertices of an equilateral triangle of side $L$. The gravitational field at the centre due to these particles is

The mass density of a planet of radius $R$ varies with the distance $r$ from its centre as $\rho(r) = \rho_{0} \left(1 - \frac{r^{2}}{R^{2}}\right)$. Then the gravitational field is maximum at: