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(C) Given: Mass of each sphere $M = 1.5\, {kg}$,radius $r = 50\, {cm} = 0.5\, {m}$,and distance between centers $L = 5\, {m}$.The axis of rotation pas

Vedclass · Accepted Answer

$19.05$

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(C) Given: Mass of each sphere $M = 1.5\, {kg}$,radius $r = 50\, {cm} = 0.5\, {m}$,and distance between centers $L = 5\, {m}$.The axis of rotation passes through the midpoint of the rod,which is also the center of mass of the system.The distance of each sphere's center from the axis of rotation is $d = L/2 = 5/2 = 2.5\, {m}$.Using the parallel axis theorem for each sphere,the moment of inertia $I$ of one sphere about the axis is $I_{sphere} = I_{cm} + Md^2 = \frac{2}{5}Mr^2 + Md^2$.Since there are two identical spheres,the total moment of inertia of the system is $I_{total} = 2 	imes (\frac{2}{5}Mr^2 + Md^2)$.Substituting the values: $I_{total} = 2 	imes [\frac{2}{5} 	imes 1.5 	imes (0.5)^2 + 1.5 	imes (2.5)^2]$.$I_{total} = 2 	imes [0.4 	imes 1.5 	imes 0.25 + 1.5 	imes 6.25]$.$I_{total} = 2 	imes [0.15 + 9.375] = 2 	imes 9.525 = 19.05\, {kgm}^{2}$.

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