1. Given

A solid sphere is rotating in free space. Its radius is increased while its mass remains the same. We need to find which quantity is not affected.

The options are:

• A: Angular velocity $\omega$
• B: Angular momentum $L$
• C: Moment of inertia $I$
• D: Rotational kinetic energy $K$

2. Key physical idea: no external torque

Since the sphere is rotating in free space, there is no external torque acting on it.

Hence, angular momentum is conserved: $L = I\omega = \text{constant}$

So the quantity that remains unchanged is expected to be angular momentum.

3. Moment of inertia of a solid sphere

For a solid sphere about its diameter, $I = \frac{2}{5}MR^2$

Here mass $M$ is constant, but radius $R$ is increased. Therefore, $I \propto R^2$

So moment of inertia changes.

Thus, option C is affected.

4. Angular velocity

Since $L = I\omega = \text{constant}$

if $I$ increases, then $\omega$ must decrease: $\omega = \frac{L}{I}$

So angular velocity changes.

Thus, option A is affected.

5. Rotational kinetic energy

Rotational kinetic energy is $K = \frac{1}{2}I\omega^2$

Using $L = I\omega$, we can write $K = \frac{L^2}{2I}$

Since $L$ is constant and $I$ increases, $K$ decreases.

So rotational kinetic energy changes.

Thus, option D is affected.

6. Angular momentum

Because no external torque acts, $L = \text{constant}$

So angular momentum is not affected.

Thus, option B is correct.

7. Check each option

• A: Angular velocity $\rightarrow$ changes
• B: Angular momentum $\rightarrow$ unchanged
• C: Moment of inertia $\rightarrow$ changes
• D: Rotational kinetic energy $\rightarrow$ changes

8. Final answer

The quantity that will not be affected is: $\boxed{\text{B: Angular momentum}}$

9. Comparison with stored correct answer

Stored correct answer: B

My derived answer: B

They agree.