For spheres each of mass M and radius R are placed with their centers on the four corners A , B , C and D of a square of side b . The spheres A and B are hollow and C and D are solids. The moment of i

Question

For spheres each of mass M and radius R are placed with their centers on the four corners A , B , C and D of a square of side b . The spheres A and B are hollow and C and D are solids. The moment of inertia of the system about side A D of square is

TestHub · Accepted Answer

Moment of inertia of a hollow sphere of

radius $R$ about the diameter passing

through $D$ is

$I_{A} = I_{B} = \frac{2}{3} M R^{2}$ ...(i)

$I_{C} = I_{D} = \frac{2}{5} M R^{2}$ ...(ii)

$∴$ Moment of inertia of whole system about side

$A D = I_{A} + I_{D} + I_{B} + I_{C}$

$= \frac{2}{3} M R^{2} + \frac{2}{5} M R^{2} + (M b^{2} + \frac{2}{3} M R^{2}) + (M b^{2} + \frac{2}{5} M R^{2})$

$= \frac{32}{15} M R^{2} + 2 M b^{2}$

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