Question

Four spheres, each of mass m and radius r, are placed with their centers on the four corners of a square side b. Calculate the moment of inertia of the system about one side of square taken as it's axis?

• A. $\frac{8}{5}{mr}^2+{2mb}^2$
• B. $\frac{8}{5}{mr}^2+{4mb}^2$
• C. $\frac{8}{5}{mr}^2+{mb}^2$
• D. None of these

Answer 1

The correct option is A $\frac{8}{5}{mr}^2+{2mb}^2$

M.I of 1,4 spheres about AB =$2\times \frac{2}{5}\times M{a}^2$

M.2 of 2,5 spheres about BC = $2\times \frac{2}{5}\times M{a}^2$

2,3 spheres about AB =$\frac{4}{5}\times M{a}^2+2M{b}^2$

$I=\frac{8}{5}\times M{a}^2+2M{b}^2$