A) \[\frac{4}{5}M{{a}^{2}}+2M{{b}^{2}}\]
B) \[\frac{8}{5}M{{a}^{2}}+2M{{b}^{2}}\]
C) \[\frac{8}{5}M{{a}^{2}}\]
D) \[\frac{4}{5}M{{a}^{2}}+4M{{b}^{2}}\]
Correct Answer: B
Solution :
[b] \[{{I}_{1}}=\frac{2}{5}M{{a}^{2}}=M.I.\] of sphere 1 about AB axis \[{{I}_{2}}=\frac{2}{5}M{{a}^{2}}=MI\] of sphere 2 about AB axis \[{{I}_{3}}=\frac{2}{5}M{{a}^{2}}+M{{b}^{2}}=M.I.\] of sphere 3 about AB axis \[{{I}_{4}}=\frac{2}{5}M{{a}^{2}}+M{{b}^{2}}=M.I.\] of sphere 4 about AB axis M.I. of system about AB axis \[{{I}_{system}}={{I}_{1}}+{{I}_{2}}+{{I}_{3}}+{{I}_{4}}\] \[=2\left( \frac{2}{5}M{{a}^{2}} \right)=2\left( \frac{2}{5}M{{a}^{2}}+M{{b}^{2}} \right)\] \[=\frac{8}{5}M{{a}^{2}}+2M{{b}^{2}}\]You need to login to perform this action.
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