$A$ 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?

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 . . . . . . .

$A$ spherical shell is cut into two pieces along a chord as shown in the figure. $P$ is a point on the plane of the chord. The magnitude of the gravitational field at $P$ due to the upper part is $I_1$ and that due to the lower part is $I_2$. What is the relation between them?

The gravitational field,due to the 'left over part' of a uniform sphere (from which a part as shown,has been 'removed out'),at a very far off point,$P$,located as shown,would be (nearly)

For the given hemispherical shell,the direction of the gravitational intensity at an arbitrary point $P$ on its rim is indicated by which arrow?

$A$ mass $m$ is placed at $P$ at a distance $h$ along the normal through the centre $O$ of a thin circular ring of mass $M$ and radius $r$. If the mass is moved further away such that $OP$ becomes $2h$,by what factor will the force of gravitation decrease,if $h = r$?