Question

A solid sphere and thin walled hollow sphere have same mass and same material. Which of them have greater moment of inertia about their diameter? [ $I_h =$ moment of inertia of hollow sphere about an axis coinciding with its diameter, $I_s =$ moment of inertia of solid sphere about an axis coinciding with its diameter]

• A. $I_s > I_h$
• B. $I_h \ge I_s$
• C. $I_h > I_s$
• D. $I_h = I_s$

Hint:

If the same mass is distributed farther from the rotation axis, moment of inertia becomes larger.

Answer 1

The Correct Option is C

Concept:
Moment of inertia depends on how far the mass is distributed from the axis. If more mass lies farther from the axis, moment of inertia is greater. ip

Step 1: Recall the standard formulas.
For a solid sphere: \[ I_s=\frac{2}{5}MR^2 \] For a thin hollow sphere: \[ I_h=\frac{2}{3}MR^2 \] ip

Step 2: Compare the two values.
Since \[ \frac{2}{3} > \frac{2}{5}, \] we get \[ I_h > I_s \] ip Hence, the correct answer is:
\[ \boxed{(C)\ I_h>I_s} \]