Three identical spherical shells, each of mass m and radius r are placed as shown in figure. |
Consider an axis XX, which is touching to two shells and passing through diameter of third shell. |
Moment of inertia of the system consisting of these three spherical shells about XX axis is [NEET 2015 ] |
A) \[\frac{11}{5}m{{r}^{2}}\]
B) \[3\,m{{r}^{2}}\]
C) \[\frac{16}{5}m{{r}^{2}}\]
D) \[4\,m{{r}^{2}}\]
Correct Answer: D
Solution :
The total moment of inertia of the system is |
\[I={{I}_{1}}+{{I}_{2}}+{{I}_{3}}\] (i) |
Hero \[{{I}_{1}}=\frac{2}{3}m{{r}^{2}}\] |
\[{{I}_{2}}={{I}_{3}}=\frac{2}{3}\,m{{r}^{2}}+m{{r}^{2}}\] |
(From parallel axis theorem] |
\[=\frac{5}{3}m{{r}^{2}}\] |
From Eq. (i), |
\[I=\frac{2}{3}m{{r}^{2}}+2\times \frac{5}{3}m{{r}^{2}}=m{{r}^{2}}\left( \frac{2}{3}+\frac{10}{3} \right)\] |
\[I=4m{{r}^{2}}\] |
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