A) 1 : 4
B) 1 : 3
C) 2 : 1
D) 1 : 1
Correct Answer: C
Solution :
After redistribution new charges on spheres are \[Q{{'}_{1}}=\left( \frac{10}{10+20} \right)\times 10=\frac{10}{3}\mu C\] and \[Q{{'}_{2}}=\left( \frac{20}{10+20} \right)\times 10=\frac{20}{3}\mu C\] Ratio of charge densities \[\frac{{{\sigma }_{1}}}{{{\sigma }_{2}}}=\frac{Q_{1}^{'}}{Q_{2}^{'}}\times \frac{{{r}_{2}}^{2}}{{{r}_{1}}^{2}}\] \[=\frac{10/3}{20/3}\times {{\left( \frac{20}{10} \right)}^{2}}=\frac{2}{1}\] \[\left\{ \sigma =\frac{Q}{4\pi {{r}^{2}}} \right\}\]
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