Question 48 of 280

A system consists of two identical spheres each of mass $1.5kg$ and radius $50cm$ at the ends of a light rod. The distance between the centres of the two spheres is $5m.$ What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint?

A$1.905\times {10}^{5}kg{m}^{2}$B$18.75kg{m}^{2}$C$19.05kg{m}^{2}$D$1.875\times {10}^{5}kg{m}^{2}$

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Answer: (C) $19.05kg{m}^{2}$

$\left.I=\left(\dfrac{2}{5}M{R}^{2}+M{x}^{2}\right)\times 2=\left[\dfrac{2}{5}\times 1.5\times {\left(0.5\right)}^{2}+1.5\times {\left(2.5\right)}^{2}\right)\right]\times 2=[0.15+9.375]\times 2=19.05{kgm}^{2}$