Question

Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :

• A. $\frac{4}{5} ma ^{2}+2 mb ^{2}$
• B. $\frac{8}{5} m a^{2}+m b^{2}$
• C. $\frac{8}{5} ma ^{2}+2 mb ^{2}$
• D. $\frac{4}{5} ma ^{2}$

Answer 1

Answer: (C)

$I =2 \times\left(\frac{2}{5} \,ma ^{2}\right)+2 \times\left(\frac{2}{5} \,ma ^{2}+ mb ^{2}\right)$
$I =\frac{8}{5} \,ma ^{2}+2 \,mb ^{2}$