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:

Infinite number of masses each of $3 \ kg$ are placed along a straight line at the distances of $1 \ m, 2 \ m, 4 \ m, 8 \ m, \ldots$ from a point $O$ on the same line. If $G$ is the universal gravitational constant,then the magnitude of gravitational field intensity at $O$ is (in $G$)

$A$ 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 mass of the moon is $\frac{M}{81}$,where $M$ is the mass of the earth. The distance between the earth and the moon is $60R$,where $R$ is the radius of the earth. At what distance from the center of the moon will the gravitational intensity be zero (in $R$)?

Define the intensity of the gravitational field and write its equation,unit,and dimensional formula.

$A$ mass $m$ is placed at point $P$ on the axis of a ring of mass $M$ and radius $R$ at a distance $R$ from its centre. The gravitational force on mass $m$ is