Two identical spheres, each of mass 2 kg and radius 50 cm, are fixed at the ends of a light rod so that the separation between their centres is 150 cm. The moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is x/(20) kg m². The value of x is .

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Accepted Answer

53. Work in metres: R=0.5 m, and each centre is (1.5)/2=0.75 m from the axis. The rod is light, so it contributes nothing. Each sphere, by the parallel-axis theorem: 2/5mR²+md²=2/5(2)(0.25)+(2)(0.5625). =0.2+1.125=1.325 kg m². Two spheres: I=2(1.325)=2.65 kg m². x/(20)=2.65, so x=53.

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