There are two bodies of masses $100 \, kg$ and $10000 \, kg$ separated by a distance of $1 \, m$. At what distance from the smaller body will the intensity of the gravitational field be zero?

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:

$A$ 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?

Two masses $90 \ kg$ and $160 \ kg$ are separated by a distance of $5 \ m$. The magnitude of the intensity of the gravitational field at a point which is at a distance $3 \ m$ from the $90 \ kg$ mass and $4 \ m$ from the $160 \ kg$ mass is (Universal gravitational constant,$G=6.67 \times 10^{-11} \ N \ m^2 \ kg^{-2}$)

$A$ uniform sphere has radius $R$ and mass $M$. The magnitude of the gravitational field at distances $r_1$ and $r_2$ from the centre of the sphere are $E_1$ and $E_2$ respectively. The ratio $E_1: E_2$ is ($r_1 > R$ and $r_2 < R$).

In a gravitational field,the gravitational potential is given by $V = -\frac{K}{x} \ (J/kg)$. The gravitational field intensity at point $(2, 0, 3) \ m$ is