Question

Four spheres each having mass $m$ and radius $r$ are placed with their centres on the four corners of a square of side $a$ . Then the moment of inertia of the system about an axis along one of the sides of the square is :-

• A. $\frac{8}{5}mr^{2}$
• B. $\frac{8}{5}mr^{2}+ma^{2}$
• C. $\frac{8}{5}mr^{2}+2ma^{2}$
• D. $\frac{4}{5}mr^{2}+4ma^{2}$

Answer 1

Answer: (C)

$I_{A B}=I_{1 A B}+I_{2 A B}+I_{3 A B}+I_{4 A B}$
$=\frac{2}{5}mr^{2}+\frac{2}{5}mr^{2}+\left(\frac{2}{5} m r^{2} + m a^{2}\right)+\left(\frac{2}{5} m r^{2} + m a^{2}\right)$
$=\frac{8}{5}mr^{2}+2ma^{2}$