A uniform solid sphere has a moment of inertia I about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center

2I/7

Explanation:

Formula for moment of inertia through the centre of mass of a solid sphere is given as; I_sc = (2/5) mR²

Now, from parallel axis theorem, moment of inertia of solid sphere from tangent is given as;

I = (2/5) m R² + m R²

I = (7/5) mR²

Thus,mR² = 5I/7

Putting 5I/7 for mR² in first equation, we have;

I_sc = (2/5) × 5I/7

I_sc = 2I/7

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