A) \[\frac{\sigma }{{{\rho }_{0}}}\]
B) \[\sqrt{2\sigma /{{\rho }_{0}}}\]
C) \[\sqrt{{{\rho }_{0}}/(2\sigma )}\]
D) \[\frac{{{\rho }_{0}}}{\sigma }\]
Correct Answer: C
Solution :
For solid sphere of radius \[{{R}_{1}}\] \[{{q}_{1}}=\int\limits_{0}^{{{R}_{1}}}{4\pi {{r}^{2}}dr\rho }\] \[=\int\limits_{0}^{{{R}_{1}}}{4\pi {{r}^{2}}dr\frac{{{\rho }_{0}}}{r}}\] \[{{q}_{1}}=4\pi \frac{R_{1}^{2}}{2}{{\rho }_{0}}\] \[{{q}_{2}}=-4\pi R_{2}^{2}\sigma \] \[{{q}_{1}}+{{q}_{2}}=0\] \[4\pi \frac{R_{1}^{2}{{\rho }_{0}}}{2}-4\pi R_{2}^{2}\sigma =0\] \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}=\frac{2\sigma }{{{\rho }_{0}}}\] \[\frac{{{R}_{2}}}{{{R}_{1}}}=\sqrt{\frac{{{\rho }_{0}}}{2\sigma }}\]
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