A solid sphere and a disc of same mass M and | vedclass

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(C) The moment of inertia of a solid sphere about an axis passing through its center is $I_{cm, sphere} = \frac{2}{5} MR^2$. Using the parallel axis t

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$\frac{29 M R^2}{10}$

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(C) The moment of inertia of a solid sphere about an axis passing through its center is $I_{cm, sphere} = \frac{2}{5} MR^2$. Using the parallel axis theorem,the moment of inertia about the point of contact is $I_1 = I_{cm, sphere} + MR^2 = \frac{2}{5} MR^2 + MR^2 = \frac{7}{5} MR^2$.The moment of inertia of a disc about an axis passing through its center and perpendicular to its plane is $I_{cm, disc} = \frac{1}{2} MR^2$. Using the parallel axis theorem,the moment of inertia about the point of contact is $I_2 = I_{cm, disc} + MR^2 = \frac{1}{2} MR^2 + MR^2 = \frac{3}{2} MR^2$.The total moment of inertia of the system about the axis passing through the point of contact is $I = I_1 + I_2 = \left(\frac{7}{5} + \frac{3}{2}\right) MR^2 = \left(\frac{14 + 15}{10}\right) MR^2 = \frac{29 MR^2}{10}$.

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