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// R_0`
B. `sqrt(2sigma//rho_0)`
C. `sqrt(rho_0//2sigma)`
D. `rho_0//sigma`

Answer

C

Explanation

Total charge in the inner sphere
`Q_1=int_0^(R_1)rhodV =int_0^(R_1) (rho_0)/r(4pir^2)dr = 4pi(R_1^2)/2rho_0`
Total charge on outer shell
`Q_2 = -4pi R_2^2 sigma`
Since, `Q_1+Q_2=0`
`4pi (R_1^2)/(2)rho_0=4piR_2^2sigmaimplies R_2^2/(R1^2)=rho_0/(2sigma)implies R_2/R_1=sqrt((rho_0)/(2sigma))`