JEE Main 2026 — Jan 22, Shift 1 — Physics solution

JEE Main2026Jan 22, Shift 1Physics

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.m $^{2}$ .

A
0.36
B
0.72
C
0.18
D
0.63

Solution

For each solid sphere, the moment of inertia about a tangent line (perpendicular to a diameter) is $I_{t an g e n t} = \frac{2}{5} m R^{2} + m R^{2} = \frac{7}{5} m R^{2}$ by the parallel-axis theorem.

The contact point is the tangent point of both spheres simultaneously, so the total MI about that tangent line is:

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

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