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

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 $O$?

What is the gravitational field intensity at any point inside a uniform spherical shell?

$A$ thin rod of length $L$ is bent in the form of a circle. Its mass is $M$. What force will act on a mass $m$ placed at the centre of this circle? $(G = \text{universal gravitational constant})$

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 $r_1 < r < r_2$?

At what distance from the centre of the moon is the point at which the strength of the resultant gravitational field of the Earth and the Moon is equal to zero (in $,R$)? The Earth's mass is $81$ times that of the Moon,and the distance between the centres of these bodies is $60\,R$,where $R$ is the radius of the Earth.