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 $\text{ J}$)

Find the gravitational force of attraction between the ring and the sphere as shown in the diagram. The plane of the ring is perpendicular to the line joining the centres. The distance between the centres of the ring (mass $m$) and the sphere (mass $M$) is $\sqrt{8}R$,where both have an equal radius $R$.

What is the intensity of the gravitational field at the center of a spherical shell?

Which one of the following graphs correctly represents the variation of the gravitational field $(I)$ with the distance $(r)$ from the centre of a spherical shell of mass $M$ and radius $a$?

There are two bodies of masses $100 \, kg$ and $10000 \, kg$ separated by a distance of $1 \, m$. At what distance from the smaller body will the intensity of the gravitational field be zero?

The gravitational field in a region is given by $\vec{E} = (5\,N/kg)\,\hat{i} + (12\,N/kg)\,\hat{j}$. If the potential at the origin is taken to be zero,then the ratio of the potential at the points $(12\,m, 0)$ and $(0, 5\,m)$ is: