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:

The distance between the centers of the moon and the earth is $D$. If the mass of the earth is $81$ times that of the moon,at what distance from the center of the earth will the gravitational field be zero?

$A$ uniform solid sphere of mass $m$ and radius $r$ is surrounded by a uniform thin spherical shell of radius $2r$ and mass $m$. Then the gravitational field:

$A$ 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

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 $G$)

At what distance from the centre of the moon is the point at which the strength of the resultant gravitational field of the Earth and the Moon is equal to zero (in $,R$)? The Earth's mass is $81$ times that of the Moon,and the distance between the centres of these bodies is $60\,R$,where $R$ is the radius of the Earth.