Q. Four spheres of diameter $2a$ and mass $M$ are placed with their centres on the four corners of a square of side $b$. Then the moment of inertia of the system about an axis along one of the sides of the square is
A) $\frac{4}{5}Ma^{2} + 2Mb^{2}$
B) $\frac{8}{5}Ma^{2} + 2Mb^{2}$
C) $\frac{8}{5}Ma^{2}$
D) $\frac{4}{5}Ma^{2} + 4Mb^{2}$
Explanation
(b) $I_{1} = \frac{2}{5}Ma^{2} =$ M.I. of sphere 1 about $AB$ axis
$I_{2} = \frac{2}{5}Ma^{2} =$ M.I. of sphere 2 about $AB$ axis
$I_{3} = \frac{2}{5}Ma^{2} + Mb^{2} =$ M.I. of sphere 3 about $AB$ axis
$I_{4} = \frac{2}{5}Ma^{2} + Mb^{2} =$ M.I. of sphere 4 about $AB$ axis
M.I. of system about axis $AB$
$I_{system} = I_{1} + I_{2} + I_{3} + I_{4}$
$= 2\left( \frac{2}{5}Ma^{2} \right) + 2\left( \frac{2}{5}Ma^{2} + Mb^{2} \right)$
$= \frac{8}{5}Ma^{2} + 2Mb^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.