$A$ uniform sphere has radius $R$ and mass $M$. The magnitude of the gravitational field at distances $r_1$ and $r_2$ from the centre of the sphere are $E_1$ and $E_2$ respectively. The ratio $E_1: E_2$ is ($r_1 > R$ and $r_2 < R$).

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:

The density of a solid sphere of radius $R$ is $\rho(r) = 20 \frac{r^2}{R^2}$,where $r$ is the distance from its centre. If the gravitational field due to this sphere at a distance $4R$ from its centre is $E$ and $G$ is the gravitational constant,then the ratio of $\frac{E}{GR}$ is

If the gravitational potential is given by $V = (3x + 4y + 12z) \ J/kg$,then the gravitational intensity at the point $(x = 1, y = 0, z = 3)$ is ....... $N \ kg^{-1}$.

$A$ sphere of mass $M$ and radius $R_2$ has a concentric cavity of radius $R_1$ as shown in the figure. The force $F$ exerted by the sphere on a particle of mass $m$ located at a distance $r$ from the center of the sphere varies as $(0 \le r \le \infty)$. Which of the following graphs correctly represents this variation?

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?