A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10

Question

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm . The moment of inertia of this pair of spheres about the tangent passing through the point of contact is $\_\_\_\_$ $kg.m^{2}$.

Accepted Answer

$\ I = \frac{7}{5}\left\lbrack m_{1}R_{1}^{2} + m_{2}R_{2}^{2} \right\rbrack$

$${= \frac{7}{5}\left\lbrack 5(10)^{2} + 10 \times (20)^{2} \right\rbrack \times 10^{- 4} }{I = 63 \times 10^{- 2}\text{ }kg{\text{ }m}^{2} }{I = 0.63\text{ }kg{\text{ }m}^{2}}$$

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