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Question

what is the moment of inertia of a cube about its diagonal?

Joshi sir comment

$M o m e n t o f i n e r t i a o f a c u b e a b o u t a l i n e p e r p e n d i c u l a r t o i t s o n e f a c e a n d p a s \sin g t h r o u g h i t s c e n t r e i s m a^{2} / 6 s o a b o u t d i a g o n a l i n e r t i a = l^{2} I_{x} + m^{2} I_{y} + n^{2} I_{z} = (l^{2} + m^{2} + n^{2}) I_{x} (h e r e I_{x} = I_{y} = I_{z}) = I_{x} = m a^{2} / 6 l, m, n a r e d i r e c t i o n \cos i n e s o f t h r e e l i n e s p a s \sin g t h r o u g e c e n t r e o f c u b e a n d p e r p e n d i c u l a r t o e a c h o t h e r$

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