A solid sphere of radius `R_(1)` and volume charge density `rho = (rho_(0))/(r )` is enclosed by a hollow sphere of radius `R_(2)` with negative surface charge density `sigma`, such that the total charge in the system is zero . `rho_(0)` is positive constant and `r` is the distance from the centre of the sphere . The ratio `R_(2)//R_(1)` is

Options

A. `(sigma)/(rho_(0))`
B. `sqrt((2 sigma)/(rho_(0)))`
C. `sqrt((rho_(0))/(2 sigma))`
D. `(rho_(0))/(sigma)`

Answer

C

Explanation

` q_(1) = int_(0)^(R_(1)) rho xx 4 pi r^(2) dr = 4 pi int_(0)^(R_(1)) (rho_(0))/( r) xx r^(2) dr = 2 pi rho_(0) R_(1)^(2)`
and ` q_(2) = - sigma xx 4 pi R_(2)^(2)`
Given ` q_(1) + q_(2) = 0 or 2 pi rho_(0) R_(1)^(2) - sigma xx 4 pi R_(2)^(2) = 0 :. (R_(2))/(R_(1)) = sqrt((rho_(0))/(2 sigma))`