There are three concentric thin spherical shells A, B and C of radii R, 2R, and 3R. Shells A and C are given charges q and 2q and shell B is earthed. Then which of the given is correct?

As the charge inside shell zero so charge induced at surface is -q

as shell B is earthed so potential at any point p on the shell will be zero

assume charge on B is x

then charge on outer surface of A is 2q+x and inner suface is x

$V_{p }= V_{A out} + V_{B surface} + V_{c in} = zero$

$$\begin{gathered} 0 = k\frac{q}{2R} + k\frac{-q+x}{2R} + k\frac{2q}{3R} \\ then x= -\frac{4q}{3} \end{gathered}$$

$q_2= x=charge on ouer surface of B=-\frac{4q}{3}$

$q_3=-x= charge on inner surface of C=\frac{4q}{3}$

$q_4= 2q+x =charge on outer surface of C=2q+\left(-\frac{4q}{3}\right)=\frac{2q}{3}$