A) \[2\pi {{a}^{4}}\,\left( \frac{A}{4}+\frac{B}{5} \right)\]
B) \[\pi {{a}^{4}}\,\left( \frac{A}{4}+\frac{aB}{5} \right)\]
C) \[2\pi {{a}^{4}}\,\left( \frac{A}{4}+\frac{aB}{5} \right)\]
D) \[2\pi {{a}^{4}}\,\left( \frac{aA}{4}+\frac{B}{5} \right)\]
Correct Answer: C
Solution :
[c] \[I=\int{dm{{r}^{2}}}=\int{\sigma \,2\,\pi \,rdr\cdot {{r}^{2}}}\] \[\Rightarrow \,\,\,I=2\pi \int\limits_{0}^{a}{(A+Br)}\,{{r}^{3}}dr=2\pi \left[ \frac{A{{a}^{4}}}{4}+\frac{B{{a}^{5}}}{5} \right]\] \[\Rightarrow \,\,\,I=2\pi {{a}^{4}}\left[ \frac{A}{4}+\frac{Ba}{5} \right]\]
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