Rotational Motion

JEE Main level, single correct, medium

82 of 280

Question 82 of 280

Two identical spherical balls of mass MM and radius RR each are stuck on two ends of a rod of length 2R2R and mass MM(see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is

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Answer: (C) 13715MR2\dfrac{137}{15}M{R}^{2}.

Applying parallel axis theorem for the balls,
Ib=[25MR2+M(2R)2]{I}_{b}=\left[\dfrac{2}{5}M{R}^{2}+M{\left(2R\right)}^{2}\right]

Itotal=2Ib+IR{I}_{total}=2{I}_{b}+{I}_{R}
Itotal=[25MR2+M(2R)2]×2+M12(2R)2{I}_{total}=\left[\dfrac{2}{5}M{R}^{2}+M{\left(2R\right)}^{2}\right]\times 2+\dfrac{M}{12}{\left(2R\right)}^{2}

Itotal=13715MR2{I}_{total}=\dfrac{137}{15}M{R}^{2}

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