$A$ 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 bodies of mass $100 \ kg$ and $10^4 \ kg$ are lying one meter apart. At what distance from the $100 \ kg$ body will the intensity of the gravitational field be zero?

Gravitational mass is proportional to gravitational

Two identical heavy spheres are separated by a distance $10$ times their radius. Will an object placed at the mid-point of the line joining their centres be in stable equilibrium or unstable equilibrium? Give reason for your answer.

Gauss's law for gravitation is given by:

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