Two concentric spherical shells have masses $M_1$ and $M_2$ and radii $r_1$ and $r_2$ $(r_1 < r_2)$. What is the gravitational intensity at a distance $r$ from the center where $r_1 < r < r_2$?

The density of a solid sphere of radius $R$ is $\rho(r) = 20 \frac{r^2}{R^2}$,where $r$ is the distance from its centre. If the gravitational field due to this sphere at a distance $4R$ from its centre is $E$ and $G$ is the gravitational constant,then the ratio of $\frac{E}{GR}$ 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?

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,$G=6.67 \times 10^{-11} \ N \ m^2 \ kg^{-2}$)

The mass density inside a solid sphere of radius $R$ varies as $\rho(r)=\rho_0\left(\frac{r}{R}\right)^\beta$,where $\rho_0$ and $\beta$ are constants and $r$ is the distance from the centre. Let $E_1$ and $E_2$ be gravitational fields due to the sphere at distances $\frac{R}{2}$ and $2R$ from the centre of the sphere,respectively. If $\frac{E_2}{E_1}=4$,the value of $\beta$ is

$A$ 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: