Irodov 1.122 Solution

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IE Irodov 1.267

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Simultaneous rotation is happening here about 2 mutually perpendicular axes. Rotational kinetic energy is found about both the axes and their algebraic sum gives total KE.  Aliter:  In the alternative method,  KE of centre of mass(translational) about the external axis is added with KE about centre of mass (which is purely rotational). The aggregate is then added with rotational KE about it's own axis to give total KE. 
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