Question

The moment of inertia of a solid sphere about its diameter is 20 kg m². The moment of inertia of a thin spherical shell having the same mass and radius about its diameter is:

• A. 16.6 kg m²
• B. 30.3 kg m²
• C. 33.3 kg m²
• D. 66.6 kg m²

Hint:

For solid spheres and spherical shells, use the standard formulas for the moment of inertia and relate the values of mass and radius to calculate the required moments of inertia.

Answer 1

The Correct Option is C

The moment of inertia of a solid sphere about its diameter is given by: \[ I_{\text{solid sphere}} = \frac{2}{5} m r^2, \] where \( m \) is the mass and \( r \) is the radius. For a solid sphere, the moment of inertia is \( 20 \, \text{kg m}^2 \). Thus: \[ \frac{2}{5} m r^2 = 20. \] From this, we can solve for \( m r^2 \): \[ m r^2 = \frac{5 \times 20}{2} = 50. \] For a thin spherical shell, the moment of inertia about its diameter is given by: \[ I_{\text{shell}} = \frac{2}{3} m r^2. \] Substitute \( m r^2 = 50 \): \[ I_{\text{shell}} = \frac{2}{3} \times 50 = 33.3 \, \text{kg m}^2. \] Thus, the correct answer is \( 33.3 \, \text{kg m}^2 \).