Two spheres each of mass M and radius frac{R} | vedclass

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(D) Let the axis pass through the centre of sphere $1$. The distance between the centres of the two spheres is $2R$.Using the parallel axis theorem fo

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$\frac{21}{5} MR^2$

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(D) Let the axis pass through the centre of sphere $1$. The distance between the centres of the two spheres is $2R$.Using the parallel axis theorem for sphere $1$,the moment of inertia about its own centre is $I_{c1} = \frac{2}{5} M (\frac{R}{2})^2 = \frac{1}{10} MR^2$.For sphere $2$,the axis is at a distance $d = 2R$ from its centre. Using the parallel axis theorem,$I_2 = I_{c2} + Md^2 = \frac{2}{5} M (\frac{R}{2})^2 + M(2R)^2 = \frac{1}{10} MR^2 + 4MR^2 = \frac{41}{10} MR^2$.The rod is massless,so its moment of inertia is $0$.The total moment of inertia $I = I_{c1} + I_2 = \frac{1}{10} MR^2 + \frac{41}{10} MR^2 = \frac{42}{10} MR^2 = \frac{21}{5} MR^2$.

Two spheres each of mass $M$ and radius $\frac{R}{2}$ are connected at the ends of a massless rod of length $2R$. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod?

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