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 $r_1 < r < r_2$?

$3$ 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

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

If gravitational potential in a region is given by $V = 4x^2$,then the gravitational field is:

Infinite particles,each of mass $3 \ kg$,are placed at distances of $1 \ m, 2 \ m, 4 \ m, 8 \ m, \dots$ from point $O$. What is the gravitational intensity at point $O$?

The mass of the Earth is $81$ times the mass of the Moon and the distance between their centres is $R$. The distance from the centre of the Earth where the gravitational force will be zero is