Five solid spheres each of mass m and radius r are rotating about an axis A as shown in figure. Hence the moment of inertia of the system about the axis of rotation A-A' as shown in figure. Hence the moment of inertia of the system about the axis of rotation A-A' is

Step-by-step solution

Moment of inertia of a sphere about diameter is 2 5 m r^2 Moment of inertia of a sphere about it tangent using parallel axis theorem aligned & I=I_ am +m r^2= 2 5 m r^2+m r^2= 7 5 m r^2 & I_ total =3 ( 2 5 m r^2 )+2 ( 7 5 m r^2 )= 20 5 m r^2=4 m r^2 aligned