Question

Moment of inertia of solid sphere having mass M and radius R about an axis passing through diameter is I. Moment of inertia of sphere of mass 2M and radius 2R is:

• A. \( 2I \)
• B. \( 4I \)
• C. \( 8I \)
• D. \( 16I \)

Hint:

Remember that the moment of inertia is dependent on both mass and the square of the distance from the axis. For objects with the same shape but different sizes, the moment of inertia scales with the square of the scaling factor for the radius.

Answer 1

The Correct Option is B

The moment of inertia of a solid sphere of mass \( M \) and radius \( R \) about an axis passing through its diameter is given by the formula: \[ I = \frac{2}{5} M R^2 \] Now, for a sphere of mass \( 2M \) and radius \( 2R \), the moment of inertia about the same axis can be calculated using the same formula: \[ I' = \frac{2}{5} (2M) (2R)^2 = \frac{2}{5} \cdot 2M \cdot 4R^2 = \frac{8}{5} M R^2 \] Now, comparing this with the original moment of inertia: \[ I' = 4 \times \frac{2}{5} M R^2 = 4I \]
Thus, the moment of inertia for the new sphere is \( 4I \).