The moment of inertia of a solid sphere about its diameter is $20 \mathrm{~kg} \mathrm{~m}^2$. The moment of…

The moment of inertia of a solid sphere about its diameter is $20 \mathrm{~kg} \mathrm{~m}^2$. The moment of inertia of a thin spherical shell having the same mass and radius about its diameter is
  1. $16.6 \mathrm{~kg} \mathrm{~m}^2$
  2. $30.3 \mathrm{~kg} \mathrm{~m}^2$
  3. $33.3 \mathrm{~kg} \mathrm{~m}^2$
  4. $66.6 \mathrm{~kg} \mathrm{~m}^2$

Solution

For solid sphere, $I=\frac{2}{5} m r^2=20$ $\therefore \quad \mathrm{mr}^2=20 \times \frac{5}{2}=50$
For thin spherical shell, $\mathrm{I}=\frac{2}{3} \mathrm{mr}^2=\frac{2}{3} \times 50=33.3 \mathrm{~kg} \mathrm{~m}^2$

Asked in: AP EAMCET 2024 (23 May Shift 1)

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