A) \[\frac{4}{3}\,M{{l}^{2}}\]
B) \[\frac{M{{l}^{2}}}{3}\,\]
C) \[\frac{M{{l}^{2}}}{6}\,\]
D) \[\frac{2}{3}\,M{{l}^{2}}\]
Correct Answer: A
Solution :
Moment of inertia of rod AB about point \[P=\frac{1}{12}\,M{{l}^{2}}\] MI of rod AB about point \[O=\frac{M{{l}^{2}}}{12}+M{{\left( \frac{1}{2} \right)}^{2}}\] \[=\,\,\frac{1}{3}\,M{{l}^{2}}\] [by the theorem of parallel axis] and the system consists of 4 rods of similar type so by the symmetry /system \[{{I}_{system}}=\,\,\frac{4}{3}\,\,M{{l}^{2}}\]
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