Question

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping the mass the same, which one of the following will not be affected?

• A. Angular velocity
• B. Angular momentum
• C. Moment of inertia
• D. Rotational kinetic energy

Hint:

When the radius of a rotating solid sphere increases, its moment of inertia increases and its angular velocity decreases, but its angular momentum is conserved.

Answer 1

The Correct Option is A

Step 1: Effect of increasing radius.
The moment of inertia \( I \) of a solid sphere is given by: \[ I = \frac{2}{5} m r^2 \] where \( r \) is the radius and \( m \) is the mass. If the radius increases while the mass stays the same, the moment of inertia increases. Step 2: Angular velocity and angular momentum.
Angular momentum \( L \) is given by: \[ L = I \omega \] where \( \omega \) is the angular velocity. Since the moment of inertia increases, the angular velocity decreases to conserve angular momentum. Therefore, the angular velocity is affected. Step 3: Conclusion.
The only quantity that remains unaffected by an increase in radius is the **angular velocity**, which is reduced to conserve angular momentum.
Final Answer: \[ \boxed{\text{Angular velocity}} \]