Q. The rectangular block shown in the figure is rotated in turn about $x - x,y - y$ and $z - z$ axes passing through its centre of mass $O$. Its moment of inertia is
A) Same about all the three axes
B) Maximum about $z - z$ axis
C) Equal about $x - x$ and $y - y$ axes
D) Maximum about $y - y$ axis
Explanation
(b) M.I. of block about $x$ axis, $I_{x} = \frac{m}{12}(b^{2} + t^{2})$
M.I. of block about $y$ axis, $I_{y} = \frac{m}{12}(l^{2} + t^{2})$
M.I. of block about $z$ axis, $I_{z} = \frac{m}{12}(l^{2} + b^{2})$
As $I > b > t\ \therefore I_{z} > I_{y} > I_{x}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.