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Question
Find the moment of inertia of a pair of spheres, each having a mass mass m and radius r, kept in contact about the tangent passing through the point of contact.
Solution
It is given that two bodies of mass m and radius r are moving along a common tangent.
Moment of inertia of the first body about XY tangent,
\[I' = I_{com} + m r^2\]
\[\text{So, }I' = \frac{2}{5}m r^2 + m r^2 = \frac{7}{5}m r^2\]
Moment of inertia of the second body about XY tangent,
\[I'' = \frac{2}{5}m r^2 + m r^2 = \frac{7}{5}m r^2\]
Therefore, net moment of inertia,
\[I = I' + I''\]
\[I = \frac{7}{5}m r^2 + \frac{7}{5}m r^2\]
\[= \frac{14}{5}m r^2\text{ units}\]
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