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A solid sphere of radius $R_{1}$ and volume charge density $ρ = \frac{ρ_{0}}{r}$ is enclosed by a hollow sphere of radius $R_{2}$ with negative surface charge density $σ$ , such that the total charge in the system is zero. $ρ_{0}$ is positive constant and $r$ is the distance from the centre of the sphere. The ratio $R_{2} / R_{1}$ is

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$\frac{σ}{ρ_{0}}$

$\sqrt{\frac{2 σ}{ρ_{0}}}$

$\sqrt{\frac{ρ_{0}}{2 σ}}$

$\frac{ρ_{0}}{σ}$

answer is C.

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Detailed Solution

$q_{1} = \int_{0}^{R_{1}} (\frac{ρ_{0}}{r}) (4 π r^{2} d r) = \frac{4 π ρ_{0} R_{1}^{2}}{2} = 2 π ρ_{0} R_{1}^{2} q_{2} = (4 π R_{2}^{2}) σ G i v e n, q_{1} = q_{2} \frac{R_{2}}{R_{1}} = \sqrt{\frac{ρ_{0}}{2 σ}}$

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