JEE Main 2026 — Jan 28, Shift 1 — Physics solution

JEE Main2026Jan 28, Shift 1Physics

A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is $n$ cm. The value of $n$ is _____ .

Your answer

Solution

Moment of inertia of a solid sphere about a diameter: $\frac{2}{5} m R^{2}$ . By parallel axis theorem about an axis at distance $d$ from the centre:

$I = \frac{2}{5} m R^{2} + m d^{2} = m k^{2}$ , so $k^{2} = \frac{2}{5} R^{2} + d^{2}$ .

Plug $R = 10$ cm, $d = 15$ cm:

$k^{2} = \frac{2}{5} (100) + 225 = 40 + 225 = 265$ cm $^{2}$ .

$k = 265$ cm $\Rightarrow n = 265$ .

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