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 $\_\_\_\_$ $\mathrm{kg} \cdot \mathrm{m}^2$.

Professor PC Thomas Classes · Answer

Using the parallel axis theorem, the moment of inertia of a solid sphere about a tangent is $I = \frac{2}{5}mR^2 + mR^2 = \frac{7}{5}mR^2$. For the first sphere: $I_1 = 1.4 	imes 5 	imes (0.1)^2 = 0.07 	ext{ kg}\cdot	ext{m}^2$. For the second sphere: $I_2 = 1.4 	imes 10 	imes (0.2)^2 = 0.56 	ext{ kg}\cdot	ext{m}^2$. The total moment of inertia is $I = I_1 + I_2 = 0.07 + 0.56 = 0.63 	ext{ kg}\cdot	ext{m}^2$.