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 $a$?

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

$3$ 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

The mass density inside a solid sphere of radius $R$ varies as $\rho(r)=\rho_0\left(\frac{r}{R}\right)^\beta$,where $\rho_0$ and $\beta$ are constants and $r$ is the distance from the centre. Let $E_1$ and $E_2$ be gravitational fields due to the sphere at distances $\frac{R}{2}$ and $2R$ from the centre of the sphere,respectively. If $\frac{E_2}{E_1}=4$,the value of $\beta$ is

Two point masses having mass $m$ and $2m$ are placed at a distance $d$. The point on the line joining the point masses,where the gravitational field intensity is zero,will be at a distance ............

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 ....... $N \ kg^{-1}$.