Two identical solid spheres, each of mass 2 kg and radius 10 cm, are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is ×10⁻³ kg m².

Question

Accepted Answer

176. In metres: R=0.1 m, and each centre is (0.4)/2=0.2 m from the axis. Each sphere: 2/5mR²+md²=2/5(2)(0.01)+(2)(0.04). =0.008+0.08=0.088 kg m². Two spheres: I=0.176 kg m². Written as asked: 176×10⁻³ kg m². Notice that the shift term is ten times the sphere's own term here, which is why the spheres can almost, but not quite, be treated as points.

Two identical solid spheres, each of mass 2 kg and radius 10 cm, are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is ______ ×10⁻³ kg m².

Step-by-step solution