A) \[\frac{11{{R}^{2}}\rho }{24{{\varepsilon }_{0}}}\]
B) \[\frac{5}{12}\frac{{{R}^{2}}\rho }{{{\varepsilon }_{0}}}\]
C) \[\frac{7\rho {{R}^{2}}}{12{{\varepsilon }_{0}}}\]
D) \[\frac{3}{2}\frac{{{R}^{2}}\rho }{{{\varepsilon }_{0}}}\]
Correct Answer: B
Solution :
\[{{V}_{0}}=\frac{\rho }{6{{\in }_{0}}}(3{{R}^{2}}-{{0}^{2}})\] \[-\frac{\rho }{6{{\in }_{0}}}\left( 3{{\left( \frac{R}{2} \right)}^{2}}-{{\left( \frac{R}{2} \right)}^{2}} \right)\] \[=\frac{\rho }{6{{\in }_{0}}}\left( 3{{R}^{2}}-\frac{{{R}^{2}}}{2} \right)=\frac{5{{R}^{2}}\rho }{12{{\in }_{0}}}\]
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