JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Rotational Mechanics

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A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is ______ kg.m².

(A)0.36
(B)0.72
(C)0.18
(D)0.63✓ Correct

Answer: (D)

Solution

The axis is the common tangent at the point of contact, and each sphere's centre stands one radius from this line. By the parallel-axis theorem a solid sphere has

I_{tan} = \frac{2}{5} m R^{2} + m R^{2} = \frac{7}{5} m R^{2}

. Summing the two spheres,

I = \frac{7}{5} [m_{1} R_{1}^{2} + m_{2} R_{2}^{2}] = \frac{7}{5} [5 (0.1)^{2} + 10 (0.2)^{2}] = \frac{7}{5} (0.05 + 0.40) = \frac{7}{5} (0.45) = 0.63 kg m^{2} .

JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Single correct option

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