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

Step 1: Understanding the Concept:
Moment of inertia depends on mass distribution relative to the axis. For the same mass, if the mass is distributed further from the axis, the moment of inertia is greater.
Step 2: Key Formula or Approach:
$I_{solid} = \frac{2}{5} MR^2$.
$I_{hollow} = \frac{2}{3} MR^2$.
Step 3: Detailed Explanation:
For identical mass and material, a hollow sphere must have a larger external radius than a solid sphere because of the void inside. Even if radii were same, the coefficient $2/3$ (hollow) is greater than $2/5$ (solid). Thus, mass in a hollow sphere is pushed further from the diameter axis.
Step 4: Final Answer:
The hollow sphere has greater moment of inertia: $I_h>I_s$.