$A$ metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $m$ is placed at the centre of the arc. The gravitational force on the particle by the wire is:

The gravitational potential versus distance $r$ graph is represented in the figure. The magnitude of the gravitational field intensity is equal to....... $N/kg$.

An infinite number of masses,each of $1 \ kg$,are placed on the $+ve \ X$-axis at $1 \ m, 2 \ m, 4 \ m, \dots$ from the origin. The magnitude of the gravitational field at the origin due to this distribution of masses is:

$A$ spherical shell is cut into two pieces along a plane as shown in the figure. $P$ is a point on the plane of the cut. 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?

Two concentric shells of masses $m_1$ and $m_2$ have radii $r_2$ and $r_1$ respectively (where $r_2 < r_1$). $A$ particle of mass $m$ is placed at positions $A, B,$ and $C$ as shown in the figure. The gravitational forces on the particle at these positions are:

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 $R$.