Topic: Angular momentum and its conservation· Rotational Motion

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere ?

1. Angular velocity

2. Rotational kinetic energy

3. Moment of inertia

4. Angular momentum

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Answer: 4. Angular momentum

The sphere is in free space, so there is no external torque and angular momentum \(L=I\omega\) is conserved.

When the radius increases at constant mass, \(I=\tfrac25MR^2\) increases, so \(\omega\) decreases. Rotational energy \(K=\dfrac{L^2}{2I}\) also decreases. Only angular momentum stays constant.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere ?

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