A) \[\frac{8}{3}M{{R}^{2}}+2M{{b}^{2}}\]
B) \[\frac{8}{5}M{{R}^{2}}+2M{{b}^{2}}\]
C) \[\frac{32}{15}M{{R}^{2}}+2M{{b}^{2}}\]
D) \[32M{{R}^{2}}+4M{{b}^{2}}\]
Correct Answer: C
Solution :
Moment of inertia of a hollow sphere of radius R about the diameter passing through D is \[{{I}_{A}}=\frac{2}{3}M{{R}^{2}}\] ?. (i) Moment of inertia of solid sphere about diameter \[{{I}_{B}}=\frac{2}{5}M{{R}^{2}}\] ...(ii) \[\therefore \]Moment of inertia of whole system about side \[AD={{I}_{A}}+{{I}_{D}}+{{I}_{B}}+{{I}_{C}}\] \[=\frac{2}{3}M{{R}^{2}}+\frac{2}{5}M{{R}^{2}}+\left( M{{b}^{2}}+\frac{2}{3}M{{R}^{2}} \right)\] \[+\left( M{{b}^{2}}+\frac{2}{5}M{{R}^{2}} \right)\] \[=\frac{32}{15}M{{R}^{2}}+2M{{b}^{2}}\]You need to login to perform this action.
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