Three identical uniform solid spheres each of mass \(m\) and radius \(r\) are joined as shown in the figure. with centres lying in the same plane. The moment of inertia of the system about an axis lying in that plane and passing through the centre of sphere \(C\) is

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Aicharya · Accepted Answer

Moment of inertia of each solid sphere, \(I=\frac{2}{5} m r^2\)

where, \(m=\) mass and \(r=\) radius. The moment of inertia of the system about axis \(P Q\) as shown in the figure. \(I_{P Q}=I_A+I_B+I_C\) \(\begin{aligned} & =\left[\left(\frac{2}{5} m r^2\right)+m r^2\right]+\left[\left(\frac{2}{5} m r^2\right)+m r^2\right]+\left[\frac{2}{5} m r^2\right] \\ & =\frac{7}{5} m r^2+\frac{7}{5} m r^2+\frac{2}{5} m r^2=\frac{16}{5} m r^2 \end{aligned}\)

Three identical uniform solid spheres each of mass \(m\) and radius \(r\) are joined as shown in the figure.…

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