Which of the following can be derived from above theorem

parallel axis theorem

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perpendicular axis theorem

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both

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None of these

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Solution

The correct option is C perpendicular axis theorem
$F o r a p l a n a r b o d y w h i c h i s i n x - y p l a n e . I_{x} + I_{y} + I_{z} = 2 \sum m_{i} {r_{i}}^{2} = 2 \sum m_{i} ({x_{i}}^{2} + {y_{i}}^{2}) b e c u a s e t h e z c o m p o n e n t i s z e r o f o r a l l t h e p o i n t s a s t h e b o d y i n x - y p l a n e . I_{x} + I_{y} + I_{z} = 2 \sum m_{i} ({x_{i}}^{2} + {y_{i}}^{2}) = 2 (I_{y} + I_{x}) \Rightarrow I_{z} = I_{y} + I_{x}$

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