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

$A$ solid sphere of mass $M$ and radius $a$ is surrounded by a uniform concentric spherical shell of thickness $2a$ and mass $2M$. The gravitational field at distance $3a$ from the centre will be

Two concentric hollow spheres of radius $R$ and $2R$ have the same mass $M$,as shown in the figure. The gravitational field intensity at point $P$ (where $R < r < 2R$) is:

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 . . . . . . .

$3$ 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

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 $a$?