A) \[2I\]
B) \[\frac{I}{2}\]
C) \[\frac{3}{2}I\]
D) \[I\]
Correct Answer: A
Solution :
By the theorem of perpendicular axes, the moment of inertia about the central axis \[{{I}_{C}}\], will be equal to the sum of its moments of inertia about two mutually perpendicular diameters lying in its plane. Thus, \[{{I}_{d}}=I=\frac{1}{2}M{{R}^{2}}\] \[\therefore \] \[{{I}_{C}}=I+I=\frac{1}{2}M{{R}^{2}}+\frac{1}{2}M{{R}^{2}}\] \[=I+I=2I\]
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