Three concentric metallic spherical shells of radii $R, 2R, 3R$, are given charges $Q_1, Q_2, Q_3$, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, $Q_1 : Q_2 : Q_3$ is

Two metal spheres, one of radius $R$ and the other of radius $2R$, both have same surface charge density $\sigma $. They are brought in contact and separated. What will be new surface charge densities on them ?

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$

If another point charge $q_B$ is also placed at a distance $c ( > b) $ the center of shell, then choose the correct statements 

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in figure.If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the surface carries a uniform charge density $ '\sigma '$

If the outer surface of the shell is earthed, then identify the correct statement(s)

A thin-walled, spherical conducting shell $S$ of radius $R$ is given charge $Q$. The same amount of charge is also placed at its centre $C. $ Which of the following statements are correct ?