A) \[\frac{3}{2}\]
B) \[\frac{1}{2}\]
C) \[\frac{8}{5}\]
D) \[\frac{3}{5}\]
Correct Answer: C
Solution :
\[M=\int_{0}^{R}{(\rho _{0}^{r}(2\pi rdr)=2\pi {{\rho }_{0}}\frac{{{R}^{3}}}{3}}\] \[I=M{{R}^{2}}+\int\limits_{0}^{R}{2\pi {{\rho }_{0}}{{r}^{4}}dr}=M{{R}^{2}}+\frac{2\pi {{\rho }_{0}}{{R}^{5}}}{5}\] \[I=M{{R}^{2}}+\frac{3M{{R}^{2}}}{5}=\frac{8M{{R}^{2}}}{5}.\]You need to login to perform this action.
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