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

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 $r_1 < r < r_2$?

The gravitational field in a region is given by $I = (5 \hat{i} + 12 \hat{j}) \text{ N kg}^{-1}$. The change in the gravitational potential energy of an object of mass $3 \text{ kg}$ when it is taken from the origin to a point $(8 \text{ m}, -2 \text{ m})$ is (in $\text{ J}$)

What is the relationship between gravitational field intensity $(I)$ and gravitational potential $(V)$ at a point?

The net gravitational force at the centre of a square is found to be $F_{1}$ when four particles having masses $M, 2M, 3M,$ and $4M$ are placed at the four corners of the square as shown in the figure. It is $F_{2}$ when the positions of $3M$ and $4M$ are interchanged. The ratio $\frac{F_{1}}{F_{2}}$ is $\frac{\alpha}{\sqrt{5}}$. The value of $\alpha$ is . . . . . . .

$A$ 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? $(G = \text{universal gravitational constant})$