JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Rotational Mechanics

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

(A) $1.905 \times 1 0^{5} kg m^{2}$
(B) $1.875 \times 1 0^{5} kg m^{2}$
(C) $18.75 kg m^{2}$
(D) $19.05 kg m^{2}$ ✓ Correct

Answer: (D)

Solution

Each sphere has moment of inertia

\frac{2}{5} m R^{2}

about its own centre and lies

2.5

m from the midpoint axis. By the parallel-axis theorem one sphere contributes

\frac{2}{5} (1.5) (0.5)^{2} + (1.5) (2.5)^{2} = 0.15 + 9.375 = 9.525 kg\cdotm^{2} .

For the two spheres,

I = 2 (9.525) = 19.05 kg\cdotm^{2} .

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Single correct option

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