Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in figure. Con

Question

Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in figure. Consider an axis $X X^{\prime}$ which is touching the two shells and passing through the diameter of the third shell. Moment of inertia of the system consisting of these three spherical shells\ about $X X^{\prime}$ axis is\

Professor PC Thomas Classes · Answer

(b) : Net moment of inertia of the system, $$ I=I_{1}+I_{2}+I_{3} . $$ The moment of inertia of a shell about its diameter, $$ I_{1}=\frac{2}{3} m r^{2} . $$ The moment of inertia of a shell about its tangent is given by\ $I_{2}=I_{3}=I_{1}+m r^{2}=\frac{2}{3} m r^{2}+m r^{2}=\frac{5}{3} m r^{2}$\ $	herefore \quad I=2 	imes \frac{5}{3} m r^{2}+\frac{2}{3} m r^{2}=\frac{12 m r^{2}}{3}=4 m r^{2}$\