A) \[\frac{{{l}^{2}}}{2}\left( M+\frac{m}{4} \right)\]
B) \[\frac{{{l}^{2}}}{2}\left( \frac{M}{4}+m \right)\]
C) \[\frac{{{l}^{2}}}{4}\left[ M+\frac{m}{4} \right]\]
D) \[\frac{{{l}^{2}}}{4}\left[ \frac{M}{4}+m \right]\]
Correct Answer: A
Solution :
Moment of inertia of mass M about axis \[=M\times {{\left( \frac{l}{2} \right)}^{2}}\] Moment of inertia of both the masses having mass\[M=2M\times {{\left( \frac{l}{2} \right)}^{2}}=\frac{M{{l}^{2}}}{2}\] Moment of inertia of masses having mass \[m=2\times m{{\left( \frac{l}{4} \right)}^{2}}=\frac{m{{l}^{2}}}{8}\] Therefore, total moment of inertia \[=\frac{M{{l}^{2}}}{2}+\frac{m{{l}^{2}}}{8}\] \[=\frac{{{l}^{2}}}{2}\left[ M+\frac{m}{4} \right]\]
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